Properties

Label 2156.2
Level 2156
Weight 2
Dimension 76805
Nonzero newspaces 32
Sturm bound 564480
Trace bound 5

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Defining parameters

Level: \( N \) = \( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(564480\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2156))\).

Total New Old
Modular forms 144120 78553 65567
Cusp forms 138121 76805 61316
Eisenstein series 5999 1748 4251

Trace form

\( 76805 q - 125 q^{2} - 4 q^{3} - 125 q^{4} - 262 q^{5} - 113 q^{6} - 8 q^{7} - 209 q^{8} - 252 q^{9} + O(q^{10}) \) \( 76805 q - 125 q^{2} - 4 q^{3} - 125 q^{4} - 262 q^{5} - 113 q^{6} - 8 q^{7} - 209 q^{8} - 252 q^{9} - 84 q^{10} + q^{11} - 220 q^{12} - 215 q^{13} - 120 q^{14} + 24 q^{15} - 57 q^{16} - 257 q^{17} - 76 q^{18} + 19 q^{19} - 88 q^{20} - 266 q^{21} - 242 q^{22} - 7 q^{23} - 131 q^{24} - 208 q^{25} - 136 q^{26} - 40 q^{27} - 192 q^{28} - 399 q^{29} - 132 q^{30} + 28 q^{31} - 120 q^{32} - 260 q^{33} - 288 q^{34} + 30 q^{35} - 186 q^{36} - 112 q^{37} - 66 q^{38} + 95 q^{39} - 100 q^{40} - 79 q^{41} - 114 q^{42} + 42 q^{43} - 133 q^{44} - 252 q^{45} - 90 q^{46} + 115 q^{47} - 210 q^{48} - 140 q^{49} - 363 q^{50} + 161 q^{51} - 118 q^{52} - 181 q^{53} - 180 q^{54} + 79 q^{55} - 300 q^{56} - 427 q^{57} - 102 q^{58} + 68 q^{59} - 116 q^{60} - 141 q^{61} - 38 q^{62} + 126 q^{63} - 101 q^{64} - 2 q^{65} - 81 q^{66} + 163 q^{67} - 48 q^{68} + 133 q^{69} - 126 q^{70} + 260 q^{71} - 123 q^{72} + 73 q^{73} - 116 q^{74} + 459 q^{75} - 168 q^{76} - 207 q^{77} - 602 q^{78} + 237 q^{79} - 350 q^{80} + 181 q^{81} - 305 q^{82} + 83 q^{83} - 600 q^{84} - 267 q^{85} - 529 q^{86} - 62 q^{87} - 409 q^{88} - 473 q^{89} - 956 q^{90} - 94 q^{91} - 510 q^{92} - 528 q^{93} - 636 q^{94} - 289 q^{95} - 918 q^{96} - 568 q^{97} - 756 q^{98} - 134 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2156))\)

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
2156.2.a \(\chi_{2156}(1, \cdot)\) 2156.2.a.a 1 1
2156.2.a.b 1
2156.2.a.c 2
2156.2.a.d 2
2156.2.a.e 2
2156.2.a.f 2
2156.2.a.g 3
2156.2.a.h 3
2156.2.a.i 3
2156.2.a.j 3
2156.2.a.k 3
2156.2.a.l 4
2156.2.a.m 4
2156.2.c \(\chi_{2156}(1077, \cdot)\) 2156.2.c.a 8 1
2156.2.c.b 16
2156.2.c.c 16
2156.2.d \(\chi_{2156}(1275, \cdot)\) n/a 236 1
2156.2.f \(\chi_{2156}(1959, \cdot)\) n/a 200 1
2156.2.i \(\chi_{2156}(177, \cdot)\) 2156.2.i.a 2 2
2156.2.i.b 2
2156.2.i.c 2
2156.2.i.d 2
2156.2.i.e 4
2156.2.i.f 4
2156.2.i.g 4
2156.2.i.h 4
2156.2.i.i 4
2156.2.i.j 6
2156.2.i.k 6
2156.2.i.l 6
2156.2.i.m 6
2156.2.i.n 8
2156.2.i.o 8
2156.2.j \(\chi_{2156}(785, \cdot)\) n/a 164 4
2156.2.l \(\chi_{2156}(815, \cdot)\) n/a 400 2
2156.2.n \(\chi_{2156}(263, \cdot)\) n/a 464 2
2156.2.q \(\chi_{2156}(901, \cdot)\) 2156.2.q.a 8 2
2156.2.q.b 8
2156.2.q.c 16
2156.2.q.d 16
2156.2.q.e 32
2156.2.r \(\chi_{2156}(309, \cdot)\) n/a 288 6
2156.2.u \(\chi_{2156}(587, \cdot)\) n/a 928 4
2156.2.w \(\chi_{2156}(491, \cdot)\) n/a 944 4
2156.2.x \(\chi_{2156}(293, \cdot)\) n/a 160 4
2156.2.bb \(\chi_{2156}(111, \cdot)\) n/a 1680 6
2156.2.bd \(\chi_{2156}(43, \cdot)\) n/a 1992 6
2156.2.be \(\chi_{2156}(153, \cdot)\) n/a 336 6
2156.2.bg \(\chi_{2156}(361, \cdot)\) n/a 320 8
2156.2.bh \(\chi_{2156}(221, \cdot)\) n/a 552 12
2156.2.bi \(\chi_{2156}(117, \cdot)\) n/a 320 8
2156.2.bl \(\chi_{2156}(79, \cdot)\) n/a 1856 8
2156.2.bn \(\chi_{2156}(31, \cdot)\) n/a 1856 8
2156.2.bp \(\chi_{2156}(113, \cdot)\) n/a 1344 24
2156.2.bq \(\chi_{2156}(241, \cdot)\) n/a 672 12
2156.2.bt \(\chi_{2156}(219, \cdot)\) n/a 3984 12
2156.2.bv \(\chi_{2156}(199, \cdot)\) n/a 3360 12
2156.2.by \(\chi_{2156}(13, \cdot)\) n/a 1344 24
2156.2.bz \(\chi_{2156}(127, \cdot)\) n/a 7968 24
2156.2.cb \(\chi_{2156}(27, \cdot)\) n/a 7968 24
2156.2.ce \(\chi_{2156}(9, \cdot)\) n/a 2688 48
2156.2.cg \(\chi_{2156}(3, \cdot)\) n/a 15936 48
2156.2.ci \(\chi_{2156}(39, \cdot)\) n/a 15936 48
2156.2.cl \(\chi_{2156}(17, \cdot)\) n/a 2688 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2156))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2156)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(539))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1078))\)\(^{\oplus 2}\)