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Properties

Label 468.4
Level 468
Weight 4
Dimension 8181
Nonzero newspaces 30
Sturm bound 48384
Trace bound 15

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Defining parameters

Level: \( N \) = \( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(48384\)
Trace bound: \(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(468))\).

Total New Old
Modular forms 18624 8381 10243
Cusp forms 17664 8181 9483
Eisenstein series 960 200 760

Trace form

\( 8181 q - 12 q^{2} + 6 q^{3} - 40 q^{4} - 72 q^{5} - 66 q^{6} - 40 q^{7} - 18 q^{8} - 138 q^{9} + O(q^{10}) \) \( 8181 q - 12 q^{2} + 6 q^{3} - 40 q^{4} - 72 q^{5} - 66 q^{6} - 40 q^{7} - 18 q^{8} - 138 q^{9} + 250 q^{10} + 30 q^{11} - 12 q^{12} + 36 q^{13} + 120 q^{14} + 360 q^{15} - 544 q^{16} + 537 q^{17} + 216 q^{18} + 104 q^{19} + 570 q^{20} + 444 q^{21} + 522 q^{22} - 504 q^{23} - 30 q^{24} - 551 q^{25} - 768 q^{26} - 1296 q^{27} - 1320 q^{28} + 105 q^{29} - 900 q^{30} + 752 q^{31} - 882 q^{32} + 1662 q^{33} + 1132 q^{34} + 360 q^{35} - 2070 q^{36} - 1911 q^{37} - 1818 q^{38} - 1788 q^{39} - 2480 q^{40} - 1695 q^{41} - 1488 q^{42} - 1582 q^{43} - 168 q^{44} - 2184 q^{45} + 150 q^{46} + 1284 q^{47} + 2718 q^{48} + 3752 q^{49} + 6438 q^{50} + 6126 q^{51} + 5324 q^{52} + 2592 q^{53} + 6018 q^{54} + 324 q^{55} + 7668 q^{56} + 438 q^{57} + 586 q^{58} - 1602 q^{59} + 1080 q^{60} - 3813 q^{61} - 10590 q^{62} - 10176 q^{63} - 14164 q^{64} - 4329 q^{65} - 12876 q^{66} - 466 q^{67} - 12750 q^{68} + 288 q^{69} - 3120 q^{70} + 4344 q^{71} - 3642 q^{72} + 10908 q^{73} + 4614 q^{74} + 6678 q^{75} + 14472 q^{76} + 4068 q^{77} + 15048 q^{78} + 512 q^{79} + 24264 q^{80} + 2526 q^{81} + 9490 q^{82} + 7920 q^{83} + 17556 q^{84} - 2233 q^{85} + 12942 q^{86} + 1524 q^{87} - 6558 q^{88} - 4560 q^{89} + 10056 q^{90} - 4876 q^{91} - 7572 q^{92} - 8232 q^{93} - 14070 q^{94} - 6840 q^{95} - 1764 q^{96} + 19674 q^{97} - 2250 q^{98} - 9972 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(468))\)

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
468.4.a \(\chi_{468}(1, \cdot)\) 468.4.a.a 1 1
468.4.a.b 1
468.4.a.c 1
468.4.a.d 2
468.4.a.e 2
468.4.a.f 2
468.4.a.g 2
468.4.a.h 4
468.4.b \(\chi_{468}(181, \cdot)\) 468.4.b.a 2 1
468.4.b.b 2
468.4.b.c 2
468.4.b.d 4
468.4.b.e 8
468.4.c \(\chi_{468}(287, \cdot)\) 468.4.c.a 36 1
468.4.c.b 36
468.4.h \(\chi_{468}(467, \cdot)\) 468.4.h.a 4 1
468.4.h.b 4
468.4.h.c 4
468.4.h.d 72
468.4.i \(\chi_{468}(157, \cdot)\) 468.4.i.a 36 2
468.4.i.b 36
468.4.j \(\chi_{468}(133, \cdot)\) 468.4.j.a 84 2
468.4.k \(\chi_{468}(61, \cdot)\) 468.4.k.a 84 2
468.4.l \(\chi_{468}(217, \cdot)\) 468.4.l.a 2 2
468.4.l.b 2
468.4.l.c 6
468.4.l.d 8
468.4.l.e 8
468.4.l.f 8
468.4.n \(\chi_{468}(307, \cdot)\) n/a 206 2
468.4.p \(\chi_{468}(125, \cdot)\) 468.4.p.a 28 2
468.4.s \(\chi_{468}(35, \cdot)\) n/a 168 2
468.4.t \(\chi_{468}(361, \cdot)\) 468.4.t.a 2 2
468.4.t.b 2
468.4.t.c 2
468.4.t.d 4
468.4.t.e 4
468.4.t.f 6
468.4.t.g 8
468.4.t.h 8
468.4.w \(\chi_{468}(95, \cdot)\) n/a 496 2
468.4.x \(\chi_{468}(155, \cdot)\) n/a 496 2
468.4.bc \(\chi_{468}(23, \cdot)\) n/a 496 2
468.4.bd \(\chi_{468}(191, \cdot)\) n/a 496 2
468.4.be \(\chi_{468}(49, \cdot)\) 468.4.be.a 84 2
468.4.bj \(\chi_{468}(121, \cdot)\) 468.4.bj.a 84 2
468.4.bk \(\chi_{468}(131, \cdot)\) n/a 432 2
468.4.bl \(\chi_{468}(25, \cdot)\) 468.4.bl.a 84 2
468.4.bm \(\chi_{468}(263, \cdot)\) n/a 496 2
468.4.bp \(\chi_{468}(179, \cdot)\) n/a 168 2
468.4.bs \(\chi_{468}(31, \cdot)\) n/a 992 4
468.4.bv \(\chi_{468}(89, \cdot)\) 468.4.bv.a 56 4
468.4.bw \(\chi_{468}(149, \cdot)\) n/a 168 4
468.4.bz \(\chi_{468}(41, \cdot)\) n/a 168 4
468.4.cb \(\chi_{468}(19, \cdot)\) n/a 412 4
468.4.cc \(\chi_{468}(115, \cdot)\) n/a 992 4
468.4.cf \(\chi_{468}(7, \cdot)\) n/a 992 4
468.4.cg \(\chi_{468}(5, \cdot)\) n/a 168 4

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(468))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(468)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 2}\)