Properties

Label 576.6
Level 576
Weight 6
Dimension 20421
Nonzero newspaces 16
Sturm bound 110592
Trace bound 25

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Defining parameters

Level: \( N \) = \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(110592\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(576))\).

Total New Old
Modular forms 46656 20619 26037
Cusp forms 45504 20421 25083
Eisenstein series 1152 198 954

Trace form

\( 20421 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 32 q^{6} - 20 q^{7} - 24 q^{8} - 40 q^{9} - 72 q^{10} + 586 q^{11} - 32 q^{12} - 256 q^{13} - 24 q^{14} - 24 q^{15} - 24 q^{16} - 850 q^{17} - 32 q^{18}+ \cdots - 339544 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(576))\)

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
576.6.a \(\chi_{576}(1, \cdot)\) 576.6.a.a 1 1
576.6.a.b 1
576.6.a.c 1
576.6.a.d 1
576.6.a.e 1
576.6.a.f 1
576.6.a.g 1
576.6.a.h 1
576.6.a.i 1
576.6.a.j 1
576.6.a.k 1
576.6.a.l 1
576.6.a.m 1
576.6.a.n 1
576.6.a.o 1
576.6.a.p 1
576.6.a.q 1
576.6.a.r 1
576.6.a.s 1
576.6.a.t 1
576.6.a.u 1
576.6.a.v 1
576.6.a.w 1
576.6.a.x 1
576.6.a.y 1
576.6.a.z 1
576.6.a.ba 1
576.6.a.bb 1
576.6.a.bc 1
576.6.a.bd 1
576.6.a.be 1
576.6.a.bf 1
576.6.a.bg 1
576.6.a.bh 1
576.6.a.bi 1
576.6.a.bj 2
576.6.a.bk 2
576.6.a.bl 2
576.6.a.bm 2
576.6.a.bn 2
576.6.a.bo 2
576.6.a.bp 2
576.6.c \(\chi_{576}(575, \cdot)\) 576.6.c.a 2 1
576.6.c.b 2
576.6.c.c 8
576.6.c.d 8
576.6.c.e 8
576.6.c.f 12
576.6.d \(\chi_{576}(289, \cdot)\) 576.6.d.a 2 1
576.6.d.b 4
576.6.d.c 4
576.6.d.d 4
576.6.d.e 4
576.6.d.f 8
576.6.d.g 8
576.6.d.h 8
576.6.d.i 8
576.6.f \(\chi_{576}(287, \cdot)\) 576.6.f.a 8 1
576.6.f.b 8
576.6.f.c 24
576.6.i \(\chi_{576}(193, \cdot)\) n/a 236 2
576.6.k \(\chi_{576}(145, \cdot)\) 576.6.k.a 18 2
576.6.k.b 40
576.6.k.c 40
576.6.l \(\chi_{576}(143, \cdot)\) 576.6.l.a 80 2
576.6.p \(\chi_{576}(95, \cdot)\) n/a 240 2
576.6.r \(\chi_{576}(97, \cdot)\) n/a 240 2
576.6.s \(\chi_{576}(191, \cdot)\) n/a 236 2
576.6.v \(\chi_{576}(73, \cdot)\) None 0 4
576.6.w \(\chi_{576}(71, \cdot)\) None 0 4
576.6.y \(\chi_{576}(47, \cdot)\) n/a 472 4
576.6.bb \(\chi_{576}(49, \cdot)\) n/a 472 4
576.6.bd \(\chi_{576}(37, \cdot)\) n/a 1592 8
576.6.be \(\chi_{576}(35, \cdot)\) n/a 1280 8
576.6.bg \(\chi_{576}(25, \cdot)\) None 0 8
576.6.bj \(\chi_{576}(23, \cdot)\) None 0 8
576.6.bl \(\chi_{576}(11, \cdot)\) n/a 7648 16
576.6.bm \(\chi_{576}(13, \cdot)\) n/a 7648 16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(576))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(576)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 21}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 14}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 15}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 7}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 2}\)