Properties

Label 816.4
Level 816
Weight 4
Dimension 23030
Nonzero newspaces 26
Sturm bound 147456
Trace bound 19

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Defining parameters

Level: \( N \) = \( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 26 \)
Sturm bound: \(147456\)
Trace bound: \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(816))\).

Total New Old
Modular forms 56192 23302 32890
Cusp forms 54400 23030 31370
Eisenstein series 1792 272 1520

Trace form

\( 23030 q - 14 q^{3} - 16 q^{4} - 4 q^{5} - 88 q^{6} - 96 q^{7} - 168 q^{8} - 122 q^{9} - 320 q^{10} + 120 q^{11} + 176 q^{12} - 52 q^{13} + 696 q^{14} - 324 q^{15} + 544 q^{16} + 26 q^{17} - 96 q^{18} - 112 q^{19}+ \cdots - 1336 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(816))\)

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
816.4.a \(\chi_{816}(1, \cdot)\) 816.4.a.a 1 1
816.4.a.b 1
816.4.a.c 1
816.4.a.d 1
816.4.a.e 1
816.4.a.f 1
816.4.a.g 1
816.4.a.h 1
816.4.a.i 1
816.4.a.j 1
816.4.a.k 2
816.4.a.l 2
816.4.a.m 2
816.4.a.n 2
816.4.a.o 2
816.4.a.p 2
816.4.a.q 3
816.4.a.r 3
816.4.a.s 3
816.4.a.t 3
816.4.a.u 3
816.4.a.v 3
816.4.a.w 4
816.4.a.x 4
816.4.c \(\chi_{816}(577, \cdot)\) 816.4.c.a 2 1
816.4.c.b 4
816.4.c.c 6
816.4.c.d 6
816.4.c.e 6
816.4.c.f 8
816.4.c.g 10
816.4.c.h 12
816.4.e \(\chi_{816}(239, \cdot)\) 816.4.e.a 32 1
816.4.e.b 64
816.4.f \(\chi_{816}(409, \cdot)\) None 0 1
816.4.h \(\chi_{816}(407, \cdot)\) None 0 1
816.4.j \(\chi_{816}(647, \cdot)\) None 0 1
816.4.l \(\chi_{816}(169, \cdot)\) None 0 1
816.4.o \(\chi_{816}(815, \cdot)\) n/a 108 1
816.4.r \(\chi_{816}(395, \cdot)\) n/a 856 2
816.4.s \(\chi_{816}(157, \cdot)\) n/a 432 2
816.4.u \(\chi_{816}(205, \cdot)\) n/a 384 2
816.4.w \(\chi_{816}(203, \cdot)\) n/a 856 2
816.4.y \(\chi_{816}(455, \cdot)\) None 0 2
816.4.ba \(\chi_{816}(217, \cdot)\) None 0 2
816.4.bd \(\chi_{816}(625, \cdot)\) n/a 108 2
816.4.bf \(\chi_{816}(47, \cdot)\) n/a 216 2
816.4.bh \(\chi_{816}(35, \cdot)\) n/a 768 2
816.4.bj \(\chi_{816}(373, \cdot)\) n/a 432 2
816.4.bl \(\chi_{816}(13, \cdot)\) n/a 432 2
816.4.bm \(\chi_{816}(251, \cdot)\) n/a 856 2
816.4.bq \(\chi_{816}(49, \cdot)\) n/a 216 4
816.4.br \(\chi_{816}(287, \cdot)\) n/a 432 4
816.4.bs \(\chi_{816}(155, \cdot)\) n/a 1712 4
816.4.bt \(\chi_{816}(229, \cdot)\) n/a 864 4
816.4.bw \(\chi_{816}(59, \cdot)\) n/a 1712 4
816.4.bx \(\chi_{816}(325, \cdot)\) n/a 864 4
816.4.ca \(\chi_{816}(25, \cdot)\) None 0 4
816.4.cb \(\chi_{816}(263, \cdot)\) None 0 4
816.4.cf \(\chi_{816}(29, \cdot)\) n/a 3424 8
816.4.cg \(\chi_{816}(91, \cdot)\) n/a 1728 8
816.4.cj \(\chi_{816}(65, \cdot)\) n/a 848 8
816.4.ck \(\chi_{816}(31, \cdot)\) n/a 432 8
816.4.cn \(\chi_{816}(7, \cdot)\) None 0 8
816.4.co \(\chi_{816}(41, \cdot)\) None 0 8
816.4.cr \(\chi_{816}(5, \cdot)\) n/a 3424 8
816.4.cs \(\chi_{816}(139, \cdot)\) n/a 1728 8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(816))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(816)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(408))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(816))\)\(^{\oplus 1}\)