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Properties

Label 285.4
Level 285
Weight 4
Dimension 5804
Nonzero newspaces 18
Sturm bound 23040
Trace bound 4

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Defining parameters

Level: \( N \) = \( 285 = 3 \cdot 5 \cdot 19 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(23040\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(285))\).

Total New Old
Modular forms 8928 6004 2924
Cusp forms 8352 5804 2548
Eisenstein series 576 200 376

Trace form

\( 5804 q - 8 q^{2} - 6 q^{3} + 12 q^{4} - 12 q^{5} - 54 q^{6} + 4 q^{7} + 72 q^{8} + 18 q^{9} + O(q^{10}) \) \( 5804 q - 8 q^{2} - 6 q^{3} + 12 q^{4} - 12 q^{5} - 54 q^{6} + 4 q^{7} + 72 q^{8} + 18 q^{9} + 138 q^{10} + 112 q^{11} - 810 q^{12} - 940 q^{13} - 672 q^{14} - 267 q^{15} + 1012 q^{16} + 496 q^{17} + 372 q^{18} + 1732 q^{19} + 2024 q^{20} + 1626 q^{21} + 1652 q^{22} + 504 q^{23} - 306 q^{24} - 1090 q^{25} - 3200 q^{26} - 3060 q^{27} - 10608 q^{28} - 4096 q^{29} - 3456 q^{30} - 1732 q^{31} + 1028 q^{32} + 1842 q^{33} + 5600 q^{34} + 3272 q^{35} + 7782 q^{36} + 5112 q^{37} + 9716 q^{38} + 4992 q^{39} + 4012 q^{40} + 2528 q^{41} + 2466 q^{42} + 68 q^{43} - 2356 q^{44} + 747 q^{45} - 7192 q^{46} - 4280 q^{47} - 5640 q^{48} - 7176 q^{49} - 5234 q^{50} - 4116 q^{51} - 324 q^{52} - 224 q^{53} - 4986 q^{54} - 6 q^{55} - 6054 q^{57} - 184 q^{58} - 992 q^{59} - 9144 q^{60} - 18540 q^{61} - 19884 q^{62} - 5754 q^{63} - 18900 q^{64} - 5156 q^{65} + 90 q^{66} + 580 q^{67} + 4484 q^{68} + 9846 q^{69} + 12786 q^{70} + 9296 q^{71} + 22122 q^{72} + 28280 q^{73} + 27776 q^{74} + 8736 q^{75} + 30812 q^{76} + 37368 q^{77} + 26994 q^{78} + 34684 q^{79} + 43496 q^{80} + 4734 q^{81} + 18888 q^{82} + 4104 q^{83} - 906 q^{84} - 11262 q^{85} - 20756 q^{86} - 12186 q^{87} - 46452 q^{88} - 28272 q^{89} - 22080 q^{90} - 46780 q^{91} - 62916 q^{92} - 31014 q^{93} - 53128 q^{94} - 18532 q^{95} - 4668 q^{96} - 14508 q^{97} - 24424 q^{98} - 468 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(285))\)

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
285.4.a \(\chi_{285}(1, \cdot)\) 285.4.a.a 1 1
285.4.a.b 3
285.4.a.c 3
285.4.a.d 4
285.4.a.e 4
285.4.a.f 5
285.4.a.g 5
285.4.a.h 5
285.4.a.i 6
285.4.b \(\chi_{285}(284, \cdot)\) n/a 116 1
285.4.c \(\chi_{285}(229, \cdot)\) 285.4.c.a 2 1
285.4.c.b 20
285.4.c.c 30
285.4.h \(\chi_{285}(56, \cdot)\) 285.4.h.a 80 1
285.4.i \(\chi_{285}(106, \cdot)\) 285.4.i.a 18 2
285.4.i.b 18
285.4.i.c 22
285.4.i.d 22
285.4.k \(\chi_{285}(77, \cdot)\) n/a 216 2
285.4.m \(\chi_{285}(37, \cdot)\) n/a 120 2
285.4.p \(\chi_{285}(221, \cdot)\) n/a 160 2
285.4.q \(\chi_{285}(164, \cdot)\) n/a 232 2
285.4.r \(\chi_{285}(49, \cdot)\) n/a 120 2
285.4.u \(\chi_{285}(16, \cdot)\) n/a 240 6
285.4.v \(\chi_{285}(68, \cdot)\) n/a 464 4
285.4.x \(\chi_{285}(88, \cdot)\) n/a 240 4
285.4.z \(\chi_{285}(41, \cdot)\) n/a 480 6
285.4.be \(\chi_{285}(4, \cdot)\) n/a 360 6
285.4.bf \(\chi_{285}(14, \cdot)\) n/a 696 6
285.4.bh \(\chi_{285}(13, \cdot)\) n/a 720 12
285.4.bi \(\chi_{285}(17, \cdot)\) n/a 1392 12

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(285))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(285)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 2}\)