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Properties

Label 288.4
Level 288
Weight 4
Dimension 3033
Nonzero newspaces 12
Sturm bound 18432
Trace bound 13

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Defining parameters

Level: \( N \) = \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(18432\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(288))\).

Total New Old
Modular forms 7168 3123 4045
Cusp forms 6656 3033 3623
Eisenstein series 512 90 422

Trace form

\( 3033 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 10 q^{5} - 16 q^{6} + 6 q^{7} - 12 q^{8} - 24 q^{9} + O(q^{10}) \) \( 3033 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 10 q^{5} - 16 q^{6} + 6 q^{7} - 12 q^{8} - 24 q^{9} + 84 q^{10} - 6 q^{11} - 16 q^{12} - 130 q^{13} - 220 q^{14} + 42 q^{15} - 312 q^{16} + 118 q^{17} - 16 q^{18} - 76 q^{19} + 68 q^{20} - 288 q^{21} + 184 q^{22} + 66 q^{23} - 16 q^{24} - 353 q^{25} + 8 q^{26} - 144 q^{27} + 344 q^{28} + 14 q^{29} - 80 q^{30} - 678 q^{31} + 608 q^{32} + 388 q^{33} + 520 q^{34} - 468 q^{35} - 2056 q^{36} - 1218 q^{37} - 3844 q^{38} - 258 q^{39} - 1696 q^{40} + 754 q^{41} + 1344 q^{42} + 1662 q^{43} + 4108 q^{44} + 1952 q^{45} + 4284 q^{46} + 1182 q^{47} + 4872 q^{48} + 1801 q^{49} + 4956 q^{50} + 580 q^{51} + 924 q^{52} + 2070 q^{53} + 424 q^{54} + 232 q^{55} - 2816 q^{56} - 3624 q^{57} - 4872 q^{58} - 1690 q^{59} - 6120 q^{60} - 4642 q^{61} - 4320 q^{62} - 738 q^{63} + 4920 q^{64} + 1624 q^{65} - 16 q^{66} + 1214 q^{67} + 1736 q^{68} + 4144 q^{69} + 1392 q^{70} + 2348 q^{71} - 16 q^{72} - 4114 q^{73} - 3484 q^{74} + 1988 q^{75} - 5132 q^{76} + 1924 q^{77} + 5048 q^{78} - 13478 q^{79} + 8240 q^{80} - 3064 q^{81} + 7484 q^{82} - 10986 q^{83} + 4128 q^{84} + 796 q^{85} - 1976 q^{86} - 794 q^{87} - 5000 q^{88} - 294 q^{89} - 9376 q^{90} + 15744 q^{91} - 15088 q^{92} - 16 q^{93} - 5152 q^{94} + 25352 q^{95} - 12936 q^{96} + 8286 q^{97} - 13120 q^{98} + 14726 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(288))\)

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
288.4.a \(\chi_{288}(1, \cdot)\) 288.4.a.a 1 1
288.4.a.b 1
288.4.a.c 1
288.4.a.d 1
288.4.a.e 1
288.4.a.f 1
288.4.a.g 1
288.4.a.h 1
288.4.a.i 1
288.4.a.j 1
288.4.a.k 1
288.4.a.l 2
288.4.a.m 2
288.4.c \(\chi_{288}(287, \cdot)\) 288.4.c.a 4 1
288.4.c.b 8
288.4.d \(\chi_{288}(145, \cdot)\) 288.4.d.a 2 1
288.4.d.b 2
288.4.d.c 4
288.4.d.d 6
288.4.f \(\chi_{288}(143, \cdot)\) 288.4.f.a 12 1
288.4.i \(\chi_{288}(97, \cdot)\) 288.4.i.a 8 2
288.4.i.b 12
288.4.i.c 16
288.4.i.d 18
288.4.i.e 18
288.4.k \(\chi_{288}(73, \cdot)\) None 0 2
288.4.l \(\chi_{288}(71, \cdot)\) None 0 2
288.4.p \(\chi_{288}(47, \cdot)\) 288.4.p.a 4 2
288.4.p.b 64
288.4.r \(\chi_{288}(49, \cdot)\) 288.4.r.a 68 2
288.4.s \(\chi_{288}(95, \cdot)\) 288.4.s.a 72 2
288.4.v \(\chi_{288}(37, \cdot)\) n/a 236 4
288.4.w \(\chi_{288}(35, \cdot)\) n/a 192 4
288.4.y \(\chi_{288}(23, \cdot)\) None 0 4
288.4.bb \(\chi_{288}(25, \cdot)\) None 0 4
288.4.bc \(\chi_{288}(13, \cdot)\) n/a 1136 8
288.4.bf \(\chi_{288}(11, \cdot)\) n/a 1136 8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(288))\) into lower level spaces

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