Properties

Label 165.6
Level 165
Weight 6
Dimension 3192
Nonzero newspaces 12
Sturm bound 11520
Trace bound 1

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Defining parameters

Level: \( N \) = \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(11520\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(165))\).

Total New Old
Modular forms 4960 3296 1664
Cusp forms 4640 3192 1448
Eisenstein series 320 104 216

Trace form

\( 3192 q - 8 q^{2} + 26 q^{3} - 196 q^{4} - 240 q^{5} + 242 q^{6} + 1784 q^{7} + 1096 q^{8} - 1110 q^{9} - 5640 q^{10} - 2948 q^{11} + 228 q^{12} + 7808 q^{13} + 9972 q^{14} + 10625 q^{15} + 23060 q^{16}+ \cdots + 219554 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(165))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
165.6.a \(\chi_{165}(1, \cdot)\) 165.6.a.a 3 1
165.6.a.b 3
165.6.a.c 3
165.6.a.d 3
165.6.a.e 3
165.6.a.f 5
165.6.a.g 5
165.6.a.h 7
165.6.c \(\chi_{165}(34, \cdot)\) 165.6.c.a 26 1
165.6.c.b 26
165.6.d \(\chi_{165}(164, \cdot)\) n/a 116 1
165.6.f \(\chi_{165}(131, \cdot)\) 165.6.f.a 80 1
165.6.j \(\chi_{165}(43, \cdot)\) n/a 120 2
165.6.k \(\chi_{165}(23, \cdot)\) n/a 200 2
165.6.m \(\chi_{165}(16, \cdot)\) n/a 160 4
165.6.p \(\chi_{165}(41, \cdot)\) n/a 320 4
165.6.r \(\chi_{165}(29, \cdot)\) n/a 464 4
165.6.s \(\chi_{165}(4, \cdot)\) n/a 240 4
165.6.v \(\chi_{165}(38, \cdot)\) n/a 928 8
165.6.w \(\chi_{165}(7, \cdot)\) n/a 480 8

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(165))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(165)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)