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Properties

Label 3312.2
Level 3312
Weight 2
Dimension 134069
Nonzero newspaces 32
Sturm bound 1216512
Trace bound 25

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Defining parameters

Level: \( N \) = \( 3312 = 2^{4} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(1216512\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3312))\).

Total New Old
Modular forms 309056 135769 173287
Cusp forms 299201 134069 165132
Eisenstein series 9855 1700 8155

Trace form

\( 134069 q - 120 q^{2} - 120 q^{3} - 124 q^{4} - 155 q^{5} - 160 q^{6} - 101 q^{7} - 132 q^{8} - 48 q^{9} + O(q^{10}) \) \( 134069 q - 120 q^{2} - 120 q^{3} - 124 q^{4} - 155 q^{5} - 160 q^{6} - 101 q^{7} - 132 q^{8} - 48 q^{9} - 364 q^{10} - 117 q^{11} - 160 q^{12} - 167 q^{13} - 84 q^{14} - 126 q^{15} - 76 q^{16} - 253 q^{17} - 120 q^{18} - 277 q^{19} - 20 q^{20} - 174 q^{21} - 28 q^{22} - 74 q^{23} - 272 q^{24} + 23 q^{25} - 4 q^{26} - 84 q^{27} - 284 q^{28} - 91 q^{29} - 120 q^{30} - 65 q^{31} - 60 q^{32} - 318 q^{33} - 100 q^{34} + 57 q^{35} - 152 q^{36} - 467 q^{37} - 212 q^{38} - 6 q^{39} - 236 q^{40} - 3 q^{41} - 240 q^{42} + 27 q^{43} - 292 q^{44} - 154 q^{45} - 440 q^{46} - 48 q^{47} - 264 q^{48} - 337 q^{49} - 288 q^{50} - 56 q^{51} - 244 q^{52} - 133 q^{53} - 248 q^{54} - 141 q^{55} - 324 q^{56} - 84 q^{57} - 196 q^{58} - 41 q^{59} - 376 q^{60} - 103 q^{61} - 324 q^{62} - 126 q^{63} - 220 q^{64} - 459 q^{65} - 400 q^{66} - 113 q^{67} - 292 q^{68} - 285 q^{69} - 176 q^{70} - 227 q^{71} - 384 q^{72} - 59 q^{73} - 236 q^{74} - 224 q^{75} - 52 q^{76} - 283 q^{77} - 376 q^{78} - 247 q^{79} - 388 q^{80} - 512 q^{81} - 380 q^{82} - 363 q^{83} - 448 q^{84} - 221 q^{85} - 412 q^{86} - 258 q^{87} - 268 q^{88} - 157 q^{89} - 448 q^{90} - 558 q^{91} - 224 q^{92} - 338 q^{93} - 316 q^{94} - 431 q^{95} - 296 q^{96} - 335 q^{97} - 304 q^{98} - 150 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3312))\)

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
3312.2.a \(\chi_{3312}(1, \cdot)\) 3312.2.a.a 1 1
3312.2.a.b 1
3312.2.a.c 1
3312.2.a.d 1
3312.2.a.e 1
3312.2.a.f 1
3312.2.a.g 1
3312.2.a.h 1
3312.2.a.i 1
3312.2.a.j 1
3312.2.a.k 1
3312.2.a.l 1
3312.2.a.m 1
3312.2.a.n 1
3312.2.a.o 1
3312.2.a.p 1
3312.2.a.q 1
3312.2.a.r 1
3312.2.a.s 2
3312.2.a.t 2
3312.2.a.u 2
3312.2.a.v 2
3312.2.a.w 2
3312.2.a.x 2
3312.2.a.y 2
3312.2.a.z 2
3312.2.a.ba 2
3312.2.a.bb 2
3312.2.a.bc 2
3312.2.a.bd 2
3312.2.a.be 2
3312.2.a.bf 3
3312.2.a.bg 4
3312.2.a.bh 4
3312.2.b \(\chi_{3312}(1241, \cdot)\) None 0 1
3312.2.e \(\chi_{3312}(1151, \cdot)\) 3312.2.e.a 2 1
3312.2.e.b 2
3312.2.e.c 2
3312.2.e.d 2
3312.2.e.e 2
3312.2.e.f 2
3312.2.e.g 16
3312.2.e.h 16
3312.2.f \(\chi_{3312}(1657, \cdot)\) None 0 1
3312.2.i \(\chi_{3312}(2575, \cdot)\) 3312.2.i.a 4 1
3312.2.i.b 8
3312.2.i.c 8
3312.2.i.d 8
3312.2.i.e 8
3312.2.i.f 8
3312.2.i.g 16
3312.2.j \(\chi_{3312}(2807, \cdot)\) None 0 1
3312.2.m \(\chi_{3312}(2897, \cdot)\) 3312.2.m.a 8 1
3312.2.m.b 8
3312.2.m.c 8
3312.2.m.d 24
3312.2.n \(\chi_{3312}(919, \cdot)\) None 0 1
3312.2.q \(\chi_{3312}(1105, \cdot)\) n/a 264 2
3312.2.r \(\chi_{3312}(91, \cdot)\) n/a 476 2
3312.2.u \(\chi_{3312}(829, \cdot)\) n/a 440 2
3312.2.v \(\chi_{3312}(323, \cdot)\) n/a 352 2
3312.2.y \(\chi_{3312}(413, \cdot)\) n/a 384 2
3312.2.bb \(\chi_{3312}(2023, \cdot)\) None 0 2
3312.2.bc \(\chi_{3312}(689, \cdot)\) n/a 284 2
3312.2.bf \(\chi_{3312}(599, \cdot)\) None 0 2
3312.2.bg \(\chi_{3312}(367, \cdot)\) n/a 288 2
3312.2.bj \(\chi_{3312}(553, \cdot)\) None 0 2
3312.2.bk \(\chi_{3312}(47, \cdot)\) n/a 264 2
3312.2.bn \(\chi_{3312}(137, \cdot)\) None 0 2
3312.2.bo \(\chi_{3312}(289, \cdot)\) n/a 590 10
3312.2.bq \(\chi_{3312}(875, \cdot)\) n/a 2112 4
3312.2.br \(\chi_{3312}(965, \cdot)\) n/a 2288 4
3312.2.bu \(\chi_{3312}(643, \cdot)\) n/a 2288 4
3312.2.bv \(\chi_{3312}(277, \cdot)\) n/a 2112 4
3312.2.bz \(\chi_{3312}(199, \cdot)\) None 0 10
3312.2.ca \(\chi_{3312}(17, \cdot)\) n/a 480 10
3312.2.cd \(\chi_{3312}(71, \cdot)\) None 0 10
3312.2.ce \(\chi_{3312}(559, \cdot)\) n/a 600 10
3312.2.ch \(\chi_{3312}(73, \cdot)\) None 0 10
3312.2.ci \(\chi_{3312}(719, \cdot)\) n/a 480 10
3312.2.cl \(\chi_{3312}(89, \cdot)\) None 0 10
3312.2.cm \(\chi_{3312}(49, \cdot)\) n/a 2840 20
3312.2.cn \(\chi_{3312}(53, \cdot)\) n/a 3840 20
3312.2.cq \(\chi_{3312}(35, \cdot)\) n/a 3840 20
3312.2.cr \(\chi_{3312}(325, \cdot)\) n/a 4760 20
3312.2.cu \(\chi_{3312}(19, \cdot)\) n/a 4760 20
3312.2.cv \(\chi_{3312}(281, \cdot)\) None 0 20
3312.2.cy \(\chi_{3312}(95, \cdot)\) n/a 2880 20
3312.2.cz \(\chi_{3312}(25, \cdot)\) None 0 20
3312.2.dc \(\chi_{3312}(79, \cdot)\) n/a 2880 20
3312.2.dd \(\chi_{3312}(119, \cdot)\) None 0 20
3312.2.dg \(\chi_{3312}(65, \cdot)\) n/a 2840 20
3312.2.dh \(\chi_{3312}(7, \cdot)\) None 0 20
3312.2.dl \(\chi_{3312}(13, \cdot)\) n/a 22880 40
3312.2.dm \(\chi_{3312}(43, \cdot)\) n/a 22880 40
3312.2.dp \(\chi_{3312}(5, \cdot)\) n/a 22880 40
3312.2.dq \(\chi_{3312}(59, \cdot)\) n/a 22880 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3312))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3312)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(414))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(552))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(828))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1104))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1656))\)\(^{\oplus 2}\)