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Properties

Label 576.8
Level 576
Weight 8
Dimension 28629
Nonzero newspaces 16
Sturm bound 147456
Trace bound 25

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Defining parameters

Level: \( N \) = \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(147456\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(576))\).

Total New Old
Modular forms 65088 28827 36261
Cusp forms 63936 28629 35307
Eisenstein series 1152 198 954

Trace form

\( 28629 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 32 q^{6} - 20 q^{7} - 24 q^{8} - 40 q^{9} + O(q^{10}) \) \( 28629 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 32 q^{6} - 20 q^{7} - 24 q^{8} - 40 q^{9} - 72 q^{10} - 1222 q^{11} - 32 q^{12} - 7088 q^{13} - 24 q^{14} - 24 q^{15} - 24 q^{16} - 5858 q^{17} - 32 q^{18} - 60638 q^{19} - 24 q^{20} - 32 q^{21} + 274432 q^{22} - 12 q^{23} - 32 q^{24} - 13659 q^{25} + 727936 q^{26} - 24 q^{27} + 390848 q^{28} - 103400 q^{29} - 32 q^{30} - 357500 q^{31} - 1071344 q^{32} + 8724 q^{33} + 403136 q^{34} + 876984 q^{35} - 32 q^{36} - 1070992 q^{37} + 1244896 q^{38} - 283968 q^{39} - 2686384 q^{40} + 1842082 q^{41} - 32 q^{42} + 2441618 q^{43} + 3370448 q^{44} - 2210960 q^{45} - 72 q^{46} - 6229404 q^{47} - 32 q^{48} - 2242787 q^{49} - 2317440 q^{50} + 2234416 q^{51} + 10204920 q^{52} + 11597952 q^{53} - 32 q^{54} + 16763976 q^{55} - 10737296 q^{56} - 2745416 q^{57} - 10358160 q^{58} - 7251694 q^{59} - 32 q^{60} - 922320 q^{61} + 10344408 q^{62} + 3294148 q^{63} + 22837080 q^{64} - 291580 q^{65} - 32 q^{66} + 9445798 q^{67} - 8750088 q^{68} - 17528 q^{69} - 35990328 q^{70} + 24697384 q^{71} - 32 q^{72} - 2836570 q^{73} + 4214368 q^{74} - 303776 q^{75} + 38942888 q^{76} - 2194548 q^{77} - 78695216 q^{78} + 9598892 q^{79} + 108869520 q^{80} + 54057480 q^{81} + 147943848 q^{82} + 14600542 q^{83} - 34113664 q^{84} - 55819968 q^{85} - 208606656 q^{86} - 40789136 q^{87} - 157553544 q^{88} - 100935502 q^{89} - 63468032 q^{90} + 4226276 q^{91} + 163322304 q^{92} + 57999040 q^{93} + 224074632 q^{94} + 114644568 q^{95} + 225737936 q^{96} + 144734470 q^{97} + 188307072 q^{98} + 9729704 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(576))\)

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
576.8.a \(\chi_{576}(1, \cdot)\) 576.8.a.a 1 1
576.8.a.b 1
576.8.a.c 1
576.8.a.d 1
576.8.a.e 1
576.8.a.f 1
576.8.a.g 1
576.8.a.h 1
576.8.a.i 1
576.8.a.j 1
576.8.a.k 1
576.8.a.l 1
576.8.a.m 1
576.8.a.n 1
576.8.a.o 1
576.8.a.p 1
576.8.a.q 1
576.8.a.r 1
576.8.a.s 1
576.8.a.t 1
576.8.a.u 1
576.8.a.v 1
576.8.a.w 1
576.8.a.x 1
576.8.a.y 1
576.8.a.z 1
576.8.a.ba 1
576.8.a.bb 2
576.8.a.bc 2
576.8.a.bd 2
576.8.a.be 2
576.8.a.bf 2
576.8.a.bg 2
576.8.a.bh 2
576.8.a.bi 2
576.8.a.bj 2
576.8.a.bk 2
576.8.a.bl 2
576.8.a.bm 2
576.8.a.bn 2
576.8.a.bo 2
576.8.a.bp 2
576.8.a.bq 2
576.8.a.br 2
576.8.a.bs 4
576.8.a.bt 4
576.8.c \(\chi_{576}(575, \cdot)\) 576.8.c.a 2 1
576.8.c.b 2
576.8.c.c 4
576.8.c.d 8
576.8.c.e 12
576.8.c.f 12
576.8.c.g 16
576.8.d \(\chi_{576}(289, \cdot)\) 576.8.d.a 2 1
576.8.d.b 4
576.8.d.c 4
576.8.d.d 4
576.8.d.e 4
576.8.d.f 8
576.8.d.g 8
576.8.d.h 8
576.8.d.i 12
576.8.d.j 16
576.8.f \(\chi_{576}(287, \cdot)\) 576.8.f.a 16 1
576.8.f.b 40
576.8.i \(\chi_{576}(193, \cdot)\) n/a 332 2
576.8.k \(\chi_{576}(145, \cdot)\) n/a 138 2
576.8.l \(\chi_{576}(143, \cdot)\) n/a 112 2
576.8.p \(\chi_{576}(95, \cdot)\) n/a 336 2
576.8.r \(\chi_{576}(97, \cdot)\) n/a 336 2
576.8.s \(\chi_{576}(191, \cdot)\) n/a 332 2
576.8.v \(\chi_{576}(73, \cdot)\) None 0 4
576.8.w \(\chi_{576}(71, \cdot)\) None 0 4
576.8.y \(\chi_{576}(47, \cdot)\) n/a 664 4
576.8.bb \(\chi_{576}(49, \cdot)\) n/a 664 4
576.8.bd \(\chi_{576}(37, \cdot)\) n/a 2232 8
576.8.be \(\chi_{576}(35, \cdot)\) n/a 1792 8
576.8.bg \(\chi_{576}(25, \cdot)\) None 0 8
576.8.bj \(\chi_{576}(23, \cdot)\) None 0 8
576.8.bl \(\chi_{576}(11, \cdot)\) n/a 10720 16
576.8.bm \(\chi_{576}(13, \cdot)\) n/a 10720 16

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(576))\) into lower level spaces

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