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Properties

Label 2310.2
Level 2310
Weight 2
Dimension 29863
Nonzero newspaces 48
Sturm bound 552960
Trace bound 11

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Defining parameters

Level: \( N \) = \( 2310 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(552960\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2310))\).

Total New Old
Modular forms 142080 29863 112217
Cusp forms 134401 29863 104538
Eisenstein series 7679 0 7679

Trace form

\( 29863 q - q^{2} - 17 q^{3} - 17 q^{4} - 41 q^{5} - 53 q^{6} - 105 q^{7} - q^{8} - 113 q^{9} + O(q^{10}) \) \( 29863 q - q^{2} - 17 q^{3} - 17 q^{4} - 41 q^{5} - 53 q^{6} - 105 q^{7} - q^{8} - 113 q^{9} - 49 q^{10} - 97 q^{11} - 25 q^{12} - 94 q^{13} - 9 q^{14} - 21 q^{15} - q^{16} - 130 q^{17} + 59 q^{18} - 140 q^{19} + 15 q^{20} + 15 q^{21} + 15 q^{22} - 56 q^{23} + 35 q^{24} - 65 q^{25} + 34 q^{26} + 247 q^{27} + 47 q^{28} + 82 q^{29} + 123 q^{30} - 16 q^{31} - q^{32} + 267 q^{33} + 142 q^{34} + 203 q^{35} + 83 q^{36} + 282 q^{37} + 124 q^{38} + 266 q^{39} + 23 q^{40} + 38 q^{41} + 115 q^{42} + 164 q^{43} + 95 q^{44} + 103 q^{45} + 232 q^{46} + 256 q^{47} + 15 q^{48} + 111 q^{49} + 175 q^{50} + 178 q^{51} + 242 q^{52} + 234 q^{53} + 103 q^{54} + 483 q^{55} - 33 q^{56} + 264 q^{57} + 402 q^{58} + 340 q^{59} + 119 q^{60} + 674 q^{61} + 288 q^{62} + 531 q^{63} - 17 q^{64} + 706 q^{65} + 447 q^{66} + 972 q^{67} + 270 q^{68} + 776 q^{69} + 359 q^{70} + 856 q^{71} + 79 q^{72} + 726 q^{73} + 298 q^{74} + 563 q^{75} + 204 q^{76} + 583 q^{77} + 258 q^{78} + 656 q^{79} + 39 q^{80} + 703 q^{81} + 238 q^{82} + 492 q^{83} + 151 q^{84} + 246 q^{85} + 420 q^{86} + 410 q^{87} + 151 q^{88} + 278 q^{89} + 91 q^{90} + 674 q^{91} - 24 q^{92} + 192 q^{93} + 192 q^{94} + 180 q^{95} - q^{96} + 310 q^{97} - q^{98} + 343 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2310))\)

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
2310.2.a \(\chi_{2310}(1, \cdot)\) 2310.2.a.a 1 1
2310.2.a.b 1
2310.2.a.c 1
2310.2.a.d 1
2310.2.a.e 1
2310.2.a.f 1
2310.2.a.g 1
2310.2.a.h 1
2310.2.a.i 1
2310.2.a.j 1
2310.2.a.k 1
2310.2.a.l 1
2310.2.a.m 1
2310.2.a.n 1
2310.2.a.o 1
2310.2.a.p 1
2310.2.a.q 1
2310.2.a.r 1
2310.2.a.s 1
2310.2.a.t 1
2310.2.a.u 1
2310.2.a.v 1
2310.2.a.w 2
2310.2.a.x 2
2310.2.a.y 2
2310.2.a.z 2
2310.2.a.ba 2
2310.2.a.bb 2
2310.2.a.bc 2
2310.2.a.bd 3
2310.2.d \(\chi_{2310}(769, \cdot)\) 2310.2.d.a 24 1
2310.2.d.b 24
2310.2.d.c 24
2310.2.d.d 24
2310.2.e \(\chi_{2310}(1849, \cdot)\) 2310.2.e.a 2 1
2310.2.e.b 2
2310.2.e.c 2
2310.2.e.d 2
2310.2.e.e 2
2310.2.e.f 2
2310.2.e.g 2
2310.2.e.h 4
2310.2.e.i 6
2310.2.e.j 6
2310.2.e.k 6
2310.2.e.l 6
2310.2.e.m 6
2310.2.e.n 8
2310.2.e.o 8
2310.2.f \(\chi_{2310}(881, \cdot)\) n/a 112 1
2310.2.g \(\chi_{2310}(1121, \cdot)\) 2310.2.g.a 4 1
2310.2.g.b 4
2310.2.g.c 8
2310.2.g.d 8
2310.2.g.e 12
2310.2.g.f 12
2310.2.g.g 24
2310.2.g.h 24
2310.2.j \(\chi_{2310}(419, \cdot)\) n/a 160 1
2310.2.k \(\chi_{2310}(659, \cdot)\) n/a 144 1
2310.2.p \(\chi_{2310}(1231, \cdot)\) 2310.2.p.a 4 1
2310.2.p.b 4
2310.2.p.c 12
2310.2.p.d 12
2310.2.p.e 16
2310.2.p.f 16
2310.2.q \(\chi_{2310}(331, \cdot)\) n/a 112 2
2310.2.r \(\chi_{2310}(923, \cdot)\) n/a 384 2
2310.2.u \(\chi_{2310}(617, \cdot)\) n/a 240 2
2310.2.v \(\chi_{2310}(727, \cdot)\) n/a 160 2
2310.2.y \(\chi_{2310}(43, \cdot)\) n/a 144 2
2310.2.z \(\chi_{2310}(421, \cdot)\) n/a 192 4
2310.2.bc \(\chi_{2310}(551, \cdot)\) n/a 208 2
2310.2.bd \(\chi_{2310}(1451, \cdot)\) n/a 256 2
2310.2.be \(\chi_{2310}(439, \cdot)\) n/a 192 2
2310.2.bf \(\chi_{2310}(529, \cdot)\) n/a 160 2
2310.2.bi \(\chi_{2310}(241, \cdot)\) n/a 128 2
2310.2.bn \(\chi_{2310}(89, \cdot)\) n/a 320 2
2310.2.bo \(\chi_{2310}(989, \cdot)\) n/a 384 2
2310.2.bp \(\chi_{2310}(391, \cdot)\) n/a 256 4
2310.2.bu \(\chi_{2310}(29, \cdot)\) n/a 576 4
2310.2.bv \(\chi_{2310}(839, \cdot)\) n/a 768 4
2310.2.by \(\chi_{2310}(281, \cdot)\) n/a 384 4
2310.2.bz \(\chi_{2310}(251, \cdot)\) n/a 512 4
2310.2.ca \(\chi_{2310}(169, \cdot)\) n/a 288 4
2310.2.cb \(\chi_{2310}(139, \cdot)\) n/a 384 4
2310.2.cf \(\chi_{2310}(397, \cdot)\) n/a 320 4
2310.2.cg \(\chi_{2310}(373, \cdot)\) n/a 384 4
2310.2.cj \(\chi_{2310}(593, \cdot)\) n/a 768 4
2310.2.ck \(\chi_{2310}(23, \cdot)\) n/a 640 4
2310.2.cm \(\chi_{2310}(361, \cdot)\) n/a 512 8
2310.2.cn \(\chi_{2310}(127, \cdot)\) n/a 576 8
2310.2.cq \(\chi_{2310}(97, \cdot)\) n/a 768 8
2310.2.cr \(\chi_{2310}(113, \cdot)\) n/a 1152 8
2310.2.cu \(\chi_{2310}(83, \cdot)\) n/a 1536 8
2310.2.cv \(\chi_{2310}(149, \cdot)\) n/a 1536 8
2310.2.cw \(\chi_{2310}(59, \cdot)\) n/a 1536 8
2310.2.db \(\chi_{2310}(61, \cdot)\) n/a 512 8
2310.2.de \(\chi_{2310}(289, \cdot)\) n/a 768 8
2310.2.df \(\chi_{2310}(19, \cdot)\) n/a 768 8
2310.2.dg \(\chi_{2310}(431, \cdot)\) n/a 1024 8
2310.2.dh \(\chi_{2310}(311, \cdot)\) n/a 1024 8
2310.2.dl \(\chi_{2310}(53, \cdot)\) n/a 3072 16
2310.2.dm \(\chi_{2310}(17, \cdot)\) n/a 3072 16
2310.2.dp \(\chi_{2310}(193, \cdot)\) n/a 1536 16
2310.2.dq \(\chi_{2310}(103, \cdot)\) n/a 1536 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2310))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2310)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(385))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(462))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(770))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1155))\)\(^{\oplus 2}\)