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Properties

Label 288.6
Level 288
Weight 6
Dimension 5085
Nonzero newspaces 12
Sturm bound 27648
Trace bound 13

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Defining parameters

Level: \( N \) = \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(27648\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(288))\).

Total New Old
Modular forms 11776 5175 6601
Cusp forms 11264 5085 6179
Eisenstein series 512 90 422

Trace form

\( 5085 q - 12 q^{2} - 12 q^{3} - 12 q^{4} + 26 q^{5} - 16 q^{6} - 106 q^{7} - 12 q^{8} - 24 q^{9} + O(q^{10}) \) \( 5085 q - 12 q^{2} - 12 q^{3} - 12 q^{4} + 26 q^{5} - 16 q^{6} - 106 q^{7} - 12 q^{8} - 24 q^{9} - 236 q^{10} - 6 q^{11} - 16 q^{12} + 98 q^{13} + 2468 q^{14} + 474 q^{15} + 4168 q^{16} - 2210 q^{17} - 16 q^{18} - 4748 q^{19} - 7612 q^{20} + 3264 q^{21} - 12392 q^{22} + 12018 q^{23} - 16 q^{24} + 8175 q^{25} + 12968 q^{26} - 3744 q^{27} - 2216 q^{28} - 28174 q^{29} - 272 q^{30} + 21658 q^{31} - 18592 q^{32} + 8500 q^{33} - 6264 q^{34} - 4788 q^{35} - 68872 q^{36} - 15902 q^{37} + 138044 q^{38} + 22926 q^{39} + 211552 q^{40} + 57514 q^{41} + 60864 q^{42} + 30750 q^{43} - 142196 q^{44} - 72064 q^{45} - 190020 q^{46} - 33666 q^{47} - 224760 q^{48} - 49443 q^{49} - 260580 q^{50} - 9164 q^{51} + 91548 q^{52} + 29466 q^{53} + 230632 q^{54} + 147096 q^{55} + 544768 q^{56} - 7176 q^{57} + 305688 q^{58} + 16790 q^{59} - 97512 q^{60} - 69214 q^{61} - 541728 q^{62} + 127614 q^{63} - 49224 q^{64} + 116896 q^{65} - 16 q^{66} - 36706 q^{67} - 167608 q^{68} - 252752 q^{69} - 56304 q^{70} - 204004 q^{71} - 16 q^{72} + 134118 q^{73} + 213092 q^{74} - 159484 q^{75} + 255988 q^{76} + 215332 q^{77} + 527480 q^{78} - 717830 q^{79} + 290096 q^{80} + 537704 q^{81} - 571076 q^{82} + 1481574 q^{83} - 985056 q^{84} - 188060 q^{85} - 1173848 q^{86} + 554998 q^{87} - 646408 q^{88} - 445182 q^{89} + 284384 q^{90} - 733248 q^{91} + 1192208 q^{92} - 16 q^{93} + 1380448 q^{94} - 2044408 q^{95} + 1214328 q^{96} - 268666 q^{97} + 1518464 q^{98} - 730714 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(288))\)

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
288.6.a \(\chi_{288}(1, \cdot)\) 288.6.a.a 1 1
288.6.a.b 1
288.6.a.c 1
288.6.a.d 1
288.6.a.e 1
288.6.a.f 1
288.6.a.g 1
288.6.a.h 1
288.6.a.i 1
288.6.a.j 1
288.6.a.k 1
288.6.a.l 2
288.6.a.m 2
288.6.a.n 2
288.6.a.o 2
288.6.a.p 2
288.6.a.q 2
288.6.a.r 2
288.6.c \(\chi_{288}(287, \cdot)\) 288.6.c.a 8 1
288.6.c.b 12
288.6.d \(\chi_{288}(145, \cdot)\) 288.6.d.a 2 1
288.6.d.b 4
288.6.d.c 8
288.6.d.d 10
288.6.f \(\chi_{288}(143, \cdot)\) 288.6.f.a 20 1
288.6.i \(\chi_{288}(97, \cdot)\) n/a 120 2
288.6.k \(\chi_{288}(73, \cdot)\) None 0 2
288.6.l \(\chi_{288}(71, \cdot)\) None 0 2
288.6.p \(\chi_{288}(47, \cdot)\) n/a 116 2
288.6.r \(\chi_{288}(49, \cdot)\) n/a 116 2
288.6.s \(\chi_{288}(95, \cdot)\) n/a 120 2
288.6.v \(\chi_{288}(37, \cdot)\) n/a 396 4
288.6.w \(\chi_{288}(35, \cdot)\) n/a 320 4
288.6.y \(\chi_{288}(23, \cdot)\) None 0 4
288.6.bb \(\chi_{288}(25, \cdot)\) None 0 4
288.6.bc \(\chi_{288}(13, \cdot)\) n/a 1904 8
288.6.bf \(\chi_{288}(11, \cdot)\) n/a 1904 8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(288))\) into lower level spaces

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