Properties

Label 1815.4
Level 1815
Weight 4
Dimension 234794
Nonzero newspaces 24
Sturm bound 929280
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(929280\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1815))\).

Total New Old
Modular forms 351040 236482 114558
Cusp forms 345920 234794 111126
Eisenstein series 5120 1688 3432

Trace form

\( 234794q + 4q^{2} - 96q^{3} - 204q^{4} + 6q^{5} - 70q^{6} - 120q^{7} - 356q^{8} - 428q^{9} + O(q^{10}) \) \( 234794q + 4q^{2} - 96q^{3} - 204q^{4} + 6q^{5} - 70q^{6} - 120q^{7} - 356q^{8} - 428q^{9} - 746q^{10} - 200q^{11} - 702q^{12} - 176q^{13} + 1824q^{14} + 659q^{15} + 2804q^{16} + 1240q^{17} + 266q^{18} - 2236q^{19} - 2336q^{20} - 2518q^{21} - 2720q^{22} - 1808q^{23} - 4418q^{24} - 904q^{25} + 32q^{26} + 732q^{27} + 4716q^{28} + 3588q^{29} + 4851q^{30} + 5612q^{31} + 7236q^{32} + 3510q^{33} + 6612q^{34} + 1800q^{35} + 3914q^{36} - 1600q^{37} - 2992q^{38} - 4994q^{39} - 8602q^{40} - 9244q^{41} - 17702q^{42} - 12808q^{43} - 10500q^{44} - 5469q^{45} - 13068q^{46} - 4968q^{47} - 5290q^{48} + 1650q^{49} + 7424q^{50} + 1826q^{51} + 21124q^{52} + 13872q^{53} + 1834q^{54} + 9740q^{55} + 34720q^{56} + 11966q^{57} + 19996q^{58} + 4576q^{59} + 14511q^{60} + 9056q^{61} + 10712q^{62} + 16382q^{63} + 2004q^{64} - 6032q^{65} + 7750q^{66} - 11336q^{67} - 21288q^{68} + 834q^{69} - 21370q^{70} + 6752q^{71} - 2634q^{72} + 18680q^{73} + 4424q^{74} - 4521q^{75} - 20420q^{76} - 1800q^{77} - 30450q^{78} - 16100q^{79} - 18616q^{80} - 30776q^{81} - 47308q^{82} - 29512q^{83} - 46454q^{84} - 20978q^{85} - 19456q^{86} - 21706q^{87} - 22760q^{88} - 14876q^{89} - 13701q^{90} - 27428q^{91} - 33544q^{92} - 12826q^{93} - 17924q^{94} - 21816q^{95} + 18358q^{96} + 3624q^{97} + 404q^{98} + 9440q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1815))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1815.4.a \(\chi_{1815}(1, \cdot)\) 1815.4.a.a 1 1
1815.4.a.b 1
1815.4.a.c 1
1815.4.a.d 1
1815.4.a.e 1
1815.4.a.f 1
1815.4.a.g 1
1815.4.a.h 1
1815.4.a.i 2
1815.4.a.j 2
1815.4.a.k 2
1815.4.a.l 2
1815.4.a.m 2
1815.4.a.n 2
1815.4.a.o 2
1815.4.a.p 3
1815.4.a.q 3
1815.4.a.r 3
1815.4.a.s 3
1815.4.a.t 4
1815.4.a.u 4
1815.4.a.v 4
1815.4.a.w 4
1815.4.a.x 5
1815.4.a.y 5
1815.4.a.z 6
1815.4.a.ba 6
1815.4.a.bb 6
1815.4.a.bc 7
1815.4.a.bd 7
1815.4.a.be 8
1815.4.a.bf 10
1815.4.a.bg 12
1815.4.a.bh 12
1815.4.a.bi 12
1815.4.a.bj 12
1815.4.a.bk 12
1815.4.a.bl 12
1815.4.a.bm 12
1815.4.a.bn 12
1815.4.a.bo 12
1815.4.c \(\chi_{1815}(364, \cdot)\) n/a 328 1
1815.4.d \(\chi_{1815}(1814, \cdot)\) n/a 632 1
1815.4.f \(\chi_{1815}(1451, \cdot)\) n/a 432 1
1815.4.j \(\chi_{1815}(967, \cdot)\) n/a 648 2
1815.4.k \(\chi_{1815}(122, \cdot)\) n/a 1272 2
1815.4.m \(\chi_{1815}(511, \cdot)\) n/a 864 4
1815.4.p \(\chi_{1815}(161, \cdot)\) n/a 1728 4
1815.4.r \(\chi_{1815}(239, \cdot)\) n/a 2528 4
1815.4.s \(\chi_{1815}(124, \cdot)\) n/a 1296 4
1815.4.u \(\chi_{1815}(166, \cdot)\) n/a 2640 10
1815.4.w \(\chi_{1815}(323, \cdot)\) n/a 5056 8
1815.4.x \(\chi_{1815}(112, \cdot)\) n/a 2592 8
1815.4.bb \(\chi_{1815}(131, \cdot)\) n/a 5280 10
1815.4.bd \(\chi_{1815}(164, \cdot)\) n/a 7880 10
1815.4.be \(\chi_{1815}(34, \cdot)\) n/a 3960 10
1815.4.bh \(\chi_{1815}(23, \cdot)\) n/a 15760 20
1815.4.bi \(\chi_{1815}(43, \cdot)\) n/a 7920 20
1815.4.bk \(\chi_{1815}(16, \cdot)\) n/a 10560 40
1815.4.bm \(\chi_{1815}(4, \cdot)\) n/a 15840 40
1815.4.bn \(\chi_{1815}(29, \cdot)\) n/a 31520 40
1815.4.bp \(\chi_{1815}(41, \cdot)\) n/a 21120 40
1815.4.bt \(\chi_{1815}(7, \cdot)\) n/a 31680 80
1815.4.bu \(\chi_{1815}(38, \cdot)\) n/a 63040 80

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1815))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1815)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 2}\)