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Properties

Label 465.4
Level 465
Weight 4
Dimension 15632
Nonzero newspaces 24
Sturm bound 61440
Trace bound 4

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Defining parameters

Level: \( N \) = \( 465 = 3 \cdot 5 \cdot 31 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(61440\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(465))\).

Total New Old
Modular forms 23520 15976 7544
Cusp forms 22560 15632 6928
Eisenstein series 960 344 616

Trace form

\( 15632 q - 8 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 90 q^{6} - 20 q^{7} + 72 q^{8} + 6 q^{9} + O(q^{10}) \) \( 15632 q - 8 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 90 q^{6} - 20 q^{7} + 72 q^{8} + 6 q^{9} + 102 q^{10} + 112 q^{11} - 246 q^{12} - 388 q^{13} - 528 q^{14} - 393 q^{15} - 788 q^{16} - 80 q^{17} + 378 q^{18} + 452 q^{19} + 872 q^{20} + 486 q^{21} - 4060 q^{22} - 984 q^{23} - 894 q^{24} - 262 q^{25} + 736 q^{26} - 1434 q^{27} + 6228 q^{28} + 1784 q^{29} - 492 q^{30} + 2788 q^{31} + 9848 q^{32} + 1434 q^{33} + 5396 q^{34} + 1640 q^{35} + 1302 q^{36} + 300 q^{37} - 2336 q^{38} - 1722 q^{39} - 6986 q^{40} - 4072 q^{41} - 6726 q^{42} - 3484 q^{43} - 1456 q^{44} - 297 q^{45} - 964 q^{46} - 464 q^{47} - 9360 q^{48} - 11760 q^{49} - 9458 q^{50} - 8022 q^{51} - 9048 q^{52} - 1544 q^{53} + 2052 q^{54} + 2238 q^{55} + 16740 q^{56} + 5358 q^{57} + 20408 q^{58} + 5608 q^{59} + 12198 q^{60} + 19488 q^{61} + 21648 q^{62} + 11316 q^{63} + 16812 q^{64} + 7444 q^{65} + 15768 q^{66} + 3412 q^{67} + 7676 q^{68} + 582 q^{69} + 60 q^{70} - 5584 q^{71} - 11952 q^{72} - 2620 q^{73} - 21748 q^{74} - 753 q^{75} - 37040 q^{76} - 18024 q^{77} + 4140 q^{78} + 2980 q^{79} - 2008 q^{80} + 3162 q^{81} - 7884 q^{82} - 2736 q^{83} - 12222 q^{84} - 8274 q^{85} - 8768 q^{86} - 5958 q^{87} - 4428 q^{88} + 1752 q^{89} - 16293 q^{90} - 3364 q^{91} - 2112 q^{92} - 24054 q^{93} - 6952 q^{94} - 6608 q^{95} - 35556 q^{96} - 5028 q^{97} - 808 q^{98} - 9546 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(465))\)

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
465.4.a \(\chi_{465}(1, \cdot)\) 465.4.a.a 1 1
465.4.a.b 1
465.4.a.c 1
465.4.a.d 2
465.4.a.e 4
465.4.a.f 6
465.4.a.g 6
465.4.a.h 7
465.4.a.i 7
465.4.a.j 7
465.4.a.k 9
465.4.a.l 9
465.4.c \(\chi_{465}(94, \cdot)\) 465.4.c.a 38 1
465.4.c.b 50
465.4.e \(\chi_{465}(371, \cdot)\) n/a 128 1
465.4.g \(\chi_{465}(464, \cdot)\) n/a 188 1
465.4.i \(\chi_{465}(211, \cdot)\) n/a 128 2
465.4.j \(\chi_{465}(247, \cdot)\) n/a 192 2
465.4.k \(\chi_{465}(32, \cdot)\) n/a 360 2
465.4.n \(\chi_{465}(16, \cdot)\) n/a 256 4
465.4.o \(\chi_{465}(26, \cdot)\) n/a 256 2
465.4.q \(\chi_{465}(304, \cdot)\) n/a 192 2
465.4.t \(\chi_{465}(119, \cdot)\) n/a 376 2
465.4.w \(\chi_{465}(29, \cdot)\) n/a 752 4
465.4.y \(\chi_{465}(116, \cdot)\) n/a 512 4
465.4.ba \(\chi_{465}(4, \cdot)\) n/a 384 4
465.4.be \(\chi_{465}(98, \cdot)\) n/a 752 4
465.4.bf \(\chi_{465}(37, \cdot)\) n/a 384 4
465.4.bg \(\chi_{465}(76, \cdot)\) n/a 512 8
465.4.bj \(\chi_{465}(2, \cdot)\) n/a 1504 8
465.4.bk \(\chi_{465}(58, \cdot)\) n/a 768 8
465.4.bm \(\chi_{465}(44, \cdot)\) n/a 1504 8
465.4.bp \(\chi_{465}(19, \cdot)\) n/a 768 8
465.4.br \(\chi_{465}(11, \cdot)\) n/a 1024 8
465.4.bs \(\chi_{465}(13, \cdot)\) n/a 1536 16
465.4.bt \(\chi_{465}(38, \cdot)\) n/a 3008 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(465))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(465)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 2}\)