Properties

Label 368.4
Level 368
Weight 4
Dimension 7007
Nonzero newspaces 8
Sturm bound 33792
Trace bound 5

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Defining parameters

Level: \( N \) = \( 368 = 2^{4} \cdot 23 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(33792\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(368))\).

Total New Old
Modular forms 12980 7195 5785
Cusp forms 12364 7007 5357
Eisenstein series 616 188 428

Trace form

\( 7007 q - 40 q^{2} - 37 q^{3} - 60 q^{4} - 47 q^{5} + 20 q^{6} + 15 q^{7} + 44 q^{8} + 11 q^{9} + 92 q^{10} - 157 q^{11} - 244 q^{12} - 95 q^{13} - 420 q^{14} + 231 q^{15} - 604 q^{16} - 191 q^{17} - 392 q^{18}+ \cdots - 2051 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(368))\)

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
368.4.a \(\chi_{368}(1, \cdot)\) 368.4.a.a 1 1
368.4.a.b 1
368.4.a.c 1
368.4.a.d 1
368.4.a.e 1
368.4.a.f 2
368.4.a.g 2
368.4.a.h 3
368.4.a.i 3
368.4.a.j 3
368.4.a.k 3
368.4.a.l 4
368.4.a.m 4
368.4.a.n 4
368.4.b \(\chi_{368}(185, \cdot)\) None 0 1
368.4.c \(\chi_{368}(367, \cdot)\) 368.4.c.a 12 1
368.4.c.b 24
368.4.h \(\chi_{368}(183, \cdot)\) None 0 1
368.4.i \(\chi_{368}(91, \cdot)\) n/a 284 2
368.4.j \(\chi_{368}(93, \cdot)\) n/a 264 2
368.4.m \(\chi_{368}(49, \cdot)\) n/a 350 10
368.4.n \(\chi_{368}(7, \cdot)\) None 0 10
368.4.s \(\chi_{368}(15, \cdot)\) n/a 360 10
368.4.t \(\chi_{368}(9, \cdot)\) None 0 10
368.4.w \(\chi_{368}(13, \cdot)\) n/a 2840 20
368.4.x \(\chi_{368}(11, \cdot)\) n/a 2840 20

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(368))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(368)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 2}\)