We show a non-vanishing result for the averages of L-functions associated with the orthogonal basis of the space of cusp forms of vector-valued modular forms on the full group. We also show the existence of at least one basis element whose L-function does not vanish under certain conditions.
The dimension of vector-valued modular forms of integer weight
Landau and Ramanujan approximations for divisor sums and coefficients of cusp forms
On the number of zeros of $L-$functions attached to cusp forms of half-integral weight
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