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Properties

Label 3366.2
Level 3366
Weight 2
Dimension 80150
Nonzero newspaces 40
Sturm bound 1244160
Trace bound 12

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Defining parameters

Level: \( N \) = \( 3366 = 2 \cdot 3^{2} \cdot 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(1244160\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3366))\).

Total New Old
Modular forms 316160 80150 236010
Cusp forms 305921 80150 225771
Eisenstein series 10239 0 10239

Trace form

\( 80150 q - 4 q^{2} - 12 q^{3} - 4 q^{4} + 12 q^{6} - 28 q^{7} + 8 q^{8} + 12 q^{9} + O(q^{10}) \) \( 80150 q - 4 q^{2} - 12 q^{3} - 4 q^{4} + 12 q^{6} - 28 q^{7} + 8 q^{8} + 12 q^{9} - 28 q^{10} - 30 q^{11} - 60 q^{13} - 60 q^{14} - 12 q^{16} - 64 q^{17} - 24 q^{18} - 70 q^{19} - 8 q^{20} + 24 q^{21} - 10 q^{22} + 32 q^{23} + 8 q^{24} + 28 q^{25} + 128 q^{26} + 120 q^{27} + 76 q^{28} + 96 q^{29} + 120 q^{30} + 52 q^{31} + 26 q^{32} + 182 q^{33} + 66 q^{34} + 216 q^{35} + 32 q^{36} + 24 q^{37} + 232 q^{38} + 248 q^{39} + 60 q^{40} + 372 q^{41} + 272 q^{42} + 208 q^{43} + 94 q^{44} + 296 q^{45} + 104 q^{46} + 424 q^{47} + 12 q^{48} + 276 q^{49} + 316 q^{50} + 284 q^{51} + 144 q^{52} + 532 q^{53} + 260 q^{54} + 196 q^{55} - 8 q^{56} + 492 q^{57} + 88 q^{58} + 490 q^{59} + 128 q^{60} + 148 q^{61} + 196 q^{62} + 304 q^{63} + 8 q^{64} + 304 q^{65} + 16 q^{66} + 88 q^{67} - 22 q^{68} + 160 q^{69} - 144 q^{70} - 32 q^{71} + 12 q^{72} - 40 q^{73} - 96 q^{74} + 80 q^{75} - 16 q^{76} + 92 q^{77} - 24 q^{78} - 84 q^{79} - 52 q^{80} - 116 q^{81} - 14 q^{82} - 338 q^{83} - 184 q^{84} - 38 q^{85} - 330 q^{86} - 136 q^{87} - 46 q^{88} - 120 q^{89} - 400 q^{90} + 504 q^{91} - 188 q^{92} - 144 q^{93} - 64 q^{94} - 188 q^{95} + 14 q^{97} - 366 q^{98} - 460 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3366))\)

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
3366.2.a \(\chi_{3366}(1, \cdot)\) 3366.2.a.a 1 1
3366.2.a.b 1
3366.2.a.c 1
3366.2.a.d 1
3366.2.a.e 1
3366.2.a.f 1
3366.2.a.g 1
3366.2.a.h 1
3366.2.a.i 1
3366.2.a.j 1
3366.2.a.k 1
3366.2.a.l 1
3366.2.a.m 1
3366.2.a.n 1
3366.2.a.o 1
3366.2.a.p 1
3366.2.a.q 1
3366.2.a.r 2
3366.2.a.s 2
3366.2.a.t 2
3366.2.a.u 2
3366.2.a.v 2
3366.2.a.w 2
3366.2.a.x 2
3366.2.a.y 2
3366.2.a.z 3
3366.2.a.ba 3
3366.2.a.bb 3
3366.2.a.bc 3
3366.2.a.bd 3
3366.2.a.be 4
3366.2.a.bf 4
3366.2.a.bg 4
3366.2.a.bh 4
3366.2.b \(\chi_{3366}(2177, \cdot)\) 3366.2.b.a 2 1
3366.2.b.b 2
3366.2.b.c 2
3366.2.b.d 2
3366.2.b.e 2
3366.2.b.f 2
3366.2.b.g 2
3366.2.b.h 2
3366.2.b.i 12
3366.2.b.j 12
3366.2.b.k 12
3366.2.b.l 12
3366.2.c \(\chi_{3366}(1189, \cdot)\) 3366.2.c.a 2 1
3366.2.c.b 2
3366.2.c.c 2
3366.2.c.d 2
3366.2.c.e 4
3366.2.c.f 4
3366.2.c.g 6
3366.2.c.h 6
3366.2.c.i 6
3366.2.c.j 6
3366.2.c.k 8
3366.2.c.l 8
3366.2.c.m 8
3366.2.c.n 10
3366.2.h \(\chi_{3366}(3365, \cdot)\) 3366.2.h.a 36 1
3366.2.h.b 36
3366.2.i \(\chi_{3366}(1123, \cdot)\) n/a 320 2
3366.2.k \(\chi_{3366}(395, \cdot)\) n/a 144 2
3366.2.m \(\chi_{3366}(1585, \cdot)\) n/a 148 2
3366.2.n \(\chi_{3366}(1225, \cdot)\) n/a 320 4
3366.2.o \(\chi_{3366}(1121, \cdot)\) n/a 432 2
3366.2.t \(\chi_{3366}(67, \cdot)\) n/a 360 2
3366.2.u \(\chi_{3366}(1055, \cdot)\) n/a 384 2
3366.2.w \(\chi_{3366}(1783, \cdot)\) n/a 304 4
3366.2.y \(\chi_{3366}(593, \cdot)\) n/a 288 4
3366.2.z \(\chi_{3366}(305, \cdot)\) n/a 288 4
3366.2.be \(\chi_{3366}(577, \cdot)\) n/a 360 4
3366.2.bf \(\chi_{3366}(35, \cdot)\) n/a 256 4
3366.2.bh \(\chi_{3366}(463, \cdot)\) n/a 720 4
3366.2.bj \(\chi_{3366}(659, \cdot)\) n/a 864 4
3366.2.bk \(\chi_{3366}(103, \cdot)\) n/a 1536 8
3366.2.bl \(\chi_{3366}(683, \cdot)\) n/a 480 8
3366.2.bm \(\chi_{3366}(109, \cdot)\) n/a 720 8
3366.2.bp \(\chi_{3366}(361, \cdot)\) n/a 720 8
3366.2.br \(\chi_{3366}(557, \cdot)\) n/a 576 8
3366.2.bu \(\chi_{3366}(263, \cdot)\) n/a 1728 8
3366.2.bw \(\chi_{3366}(331, \cdot)\) n/a 1440 8
3366.2.bx \(\chi_{3366}(239, \cdot)\) n/a 1536 8
3366.2.by \(\chi_{3366}(169, \cdot)\) n/a 1728 8
3366.2.cd \(\chi_{3366}(101, \cdot)\) n/a 1728 8
3366.2.ce \(\chi_{3366}(161, \cdot)\) n/a 1152 16
3366.2.cg \(\chi_{3366}(433, \cdot)\) n/a 1440 16
3366.2.ci \(\chi_{3366}(175, \cdot)\) n/a 3456 16
3366.2.cj \(\chi_{3366}(23, \cdot)\) n/a 2880 16
3366.2.cm \(\chi_{3366}(149, \cdot)\) n/a 3456 16
3366.2.co \(\chi_{3366}(115, \cdot)\) n/a 3456 16
3366.2.cs \(\chi_{3366}(73, \cdot)\) n/a 2880 32
3366.2.ct \(\chi_{3366}(71, \cdot)\) n/a 2304 32
3366.2.cu \(\chi_{3366}(25, \cdot)\) n/a 6912 32
3366.2.cw \(\chi_{3366}(83, \cdot)\) n/a 6912 32
3366.2.da \(\chi_{3366}(5, \cdot)\) n/a 13824 64
3366.2.db \(\chi_{3366}(7, \cdot)\) n/a 13824 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3366))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3366)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(187))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(306))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(374))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(561))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1122))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1683))\)\(^{\oplus 2}\)