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Properties

Label 1155.3
Level 1155
Weight 3
Dimension 59168
Nonzero newspaces 48
Sturm bound 276480
Trace bound 8

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Defining parameters

Level: \( N \) = \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(276480\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1155))\).

Total New Old
Modular forms 94080 60240 33840
Cusp forms 90240 59168 31072
Eisenstein series 3840 1072 2768

Trace form

\( 59168 q - 16 q^{2} - 56 q^{3} - 152 q^{4} - 28 q^{5} - 208 q^{6} - 120 q^{7} - 136 q^{8} - 88 q^{9} + O(q^{10}) \) \( 59168 q - 16 q^{2} - 56 q^{3} - 152 q^{4} - 28 q^{5} - 208 q^{6} - 120 q^{7} - 136 q^{8} - 88 q^{9} - 20 q^{10} + 84 q^{11} + 288 q^{12} + 96 q^{13} + 116 q^{14} - 90 q^{15} - 296 q^{16} - 8 q^{17} + 200 q^{18} - 456 q^{19} - 244 q^{20} - 208 q^{21} - 48 q^{22} + 976 q^{24} + 640 q^{25} + 1616 q^{26} + 436 q^{27} + 1504 q^{28} + 1072 q^{29} + 802 q^{30} + 1096 q^{31} + 584 q^{32} - 408 q^{33} - 576 q^{34} - 124 q^{35} - 1636 q^{36} - 656 q^{37} - 1456 q^{38} - 1668 q^{39} - 1036 q^{40} - 1376 q^{41} - 1792 q^{42} - 784 q^{43} + 584 q^{44} - 910 q^{45} + 136 q^{46} + 480 q^{47} + 516 q^{48} + 832 q^{49} + 2668 q^{50} + 1600 q^{51} + 3336 q^{52} + 1896 q^{53} + 3252 q^{54} + 1164 q^{55} + 3288 q^{56} + 3156 q^{57} + 2904 q^{58} + 1656 q^{59} + 2610 q^{60} + 2904 q^{61} + 4336 q^{62} + 2552 q^{63} + 3216 q^{64} + 80 q^{65} + 2212 q^{66} + 336 q^{67} + 1856 q^{68} + 444 q^{69} - 832 q^{70} - 672 q^{71} - 1252 q^{72} - 4896 q^{73} - 4240 q^{74} - 1652 q^{75} - 6992 q^{76} - 2420 q^{77} - 6928 q^{78} - 5256 q^{79} - 7140 q^{80} - 2400 q^{81} - 6208 q^{82} - 6032 q^{83} - 7780 q^{84} - 4464 q^{85} - 8440 q^{86} - 2952 q^{87} - 4216 q^{88} - 1840 q^{89} - 1902 q^{90} - 3192 q^{91} - 40 q^{92} - 1100 q^{93} + 3320 q^{94} + 3900 q^{95} - 2076 q^{96} + 3656 q^{97} + 2992 q^{98} + 1540 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1155))\)

We only show spaces with odd 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
1155.3.b \(\chi_{1155}(736, \cdot)\) 1155.3.b.a 96 1
1155.3.e \(\chi_{1155}(1154, \cdot)\) n/a 376 1
1155.3.g \(\chi_{1155}(386, \cdot)\) n/a 160 1
1155.3.h \(\chi_{1155}(34, \cdot)\) n/a 160 1
1155.3.j \(\chi_{1155}(496, \cdot)\) n/a 104 1
1155.3.m \(\chi_{1155}(1079, \cdot)\) n/a 240 1
1155.3.o \(\chi_{1155}(461, \cdot)\) n/a 256 1
1155.3.p \(\chi_{1155}(274, \cdot)\) n/a 144 1
1155.3.r \(\chi_{1155}(307, \cdot)\) n/a 384 2
1155.3.u \(\chi_{1155}(232, \cdot)\) n/a 240 2
1155.3.w \(\chi_{1155}(197, \cdot)\) n/a 576 2
1155.3.x \(\chi_{1155}(188, \cdot)\) n/a 640 2
1155.3.ba \(\chi_{1155}(254, \cdot)\) n/a 640 2
1155.3.bd \(\chi_{1155}(166, \cdot)\) n/a 216 2
1155.3.be \(\chi_{1155}(109, \cdot)\) n/a 384 2
1155.3.bf \(\chi_{1155}(131, \cdot)\) n/a 512 2
1155.3.bh \(\chi_{1155}(164, \cdot)\) n/a 752 2
1155.3.bk \(\chi_{1155}(571, \cdot)\) n/a 256 2
1155.3.bm \(\chi_{1155}(199, \cdot)\) n/a 320 2
1155.3.bn \(\chi_{1155}(221, \cdot)\) n/a 424 2
1155.3.bp \(\chi_{1155}(589, \cdot)\) n/a 576 4
1155.3.bq \(\chi_{1155}(41, \cdot)\) n/a 1024 4
1155.3.bs \(\chi_{1155}(344, \cdot)\) n/a 1152 4
1155.3.bv \(\chi_{1155}(181, \cdot)\) n/a 512 4
1155.3.bx \(\chi_{1155}(454, \cdot)\) n/a 768 4
1155.3.by \(\chi_{1155}(71, \cdot)\) n/a 768 4
1155.3.ca \(\chi_{1155}(314, \cdot)\) n/a 1504 4
1155.3.cd \(\chi_{1155}(106, \cdot)\) n/a 384 4
1155.3.cf \(\chi_{1155}(122, \cdot)\) n/a 1280 4
1155.3.cg \(\chi_{1155}(32, \cdot)\) n/a 1504 4
1155.3.ci \(\chi_{1155}(67, \cdot)\) n/a 640 4
1155.3.cl \(\chi_{1155}(208, \cdot)\) n/a 768 4
1155.3.co \(\chi_{1155}(377, \cdot)\) n/a 3008 8
1155.3.cp \(\chi_{1155}(8, \cdot)\) n/a 2304 8
1155.3.cr \(\chi_{1155}(148, \cdot)\) n/a 1152 8
1155.3.cu \(\chi_{1155}(13, \cdot)\) n/a 1536 8
1155.3.cw \(\chi_{1155}(86, \cdot)\) n/a 2048 8
1155.3.cx \(\chi_{1155}(124, \cdot)\) n/a 1536 8
1155.3.cz \(\chi_{1155}(46, \cdot)\) n/a 1024 8
1155.3.dc \(\chi_{1155}(194, \cdot)\) n/a 3008 8
1155.3.de \(\chi_{1155}(101, \cdot)\) n/a 2048 8
1155.3.df \(\chi_{1155}(79, \cdot)\) n/a 1536 8
1155.3.dg \(\chi_{1155}(31, \cdot)\) n/a 1024 8
1155.3.dj \(\chi_{1155}(179, \cdot)\) n/a 3008 8
1155.3.dk \(\chi_{1155}(52, \cdot)\) n/a 3072 16
1155.3.dn \(\chi_{1155}(37, \cdot)\) n/a 3072 16
1155.3.dp \(\chi_{1155}(2, \cdot)\) n/a 6016 16
1155.3.dq \(\chi_{1155}(38, \cdot)\) n/a 6016 16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1155))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1155)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(385))\)\(^{\oplus 2}\)