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Properties

Label 3362.2
Level 3362
Weight 2
Dimension 117531
Nonzero newspaces 12
Sturm bound 1412040
Trace bound 2

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Defining parameters

Level: \( N \) = \( 3362 = 2 \cdot 41^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(1412040\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3362))\).

Total New Old
Modular forms 355450 117531 237919
Cusp forms 350571 117531 233040
Eisenstein series 4879 0 4879

Trace form

\( 117531 q + q^{2} + 4 q^{3} + q^{4} + 6 q^{5} + 4 q^{6} + 8 q^{7} + q^{8} + 13 q^{9} + O(q^{10}) \) \( 117531 q + q^{2} + 4 q^{3} + q^{4} + 6 q^{5} + 4 q^{6} + 8 q^{7} + q^{8} + 13 q^{9} + 6 q^{10} + 12 q^{11} + 4 q^{12} + 14 q^{13} + 8 q^{14} + 24 q^{15} + q^{16} + 18 q^{17} + 13 q^{18} + 20 q^{19} + 6 q^{20} + 32 q^{21} + 12 q^{22} + 24 q^{23} + 4 q^{24} + 31 q^{25} + 14 q^{26} + 40 q^{27} + 8 q^{28} + 30 q^{29} - 56 q^{30} - 48 q^{31} - 19 q^{32} - 192 q^{33} - 82 q^{34} - 112 q^{35} - 27 q^{36} - 202 q^{37} - 60 q^{38} - 264 q^{39} - 74 q^{40} - 40 q^{41} - 288 q^{42} - 36 q^{43} - 68 q^{44} - 242 q^{45} - 56 q^{46} - 192 q^{47} - 36 q^{48} - 103 q^{49} - 69 q^{50} - 168 q^{51} - 6 q^{52} - 26 q^{53} - 40 q^{54} + 72 q^{55} + 8 q^{56} + 80 q^{57} + 30 q^{58} + 60 q^{59} + 24 q^{60} + 62 q^{61} + 32 q^{62} + 104 q^{63} + q^{64} + 64 q^{65} + 48 q^{66} - 52 q^{67} + 18 q^{68} - 64 q^{69} + 48 q^{70} - 88 q^{71} + 13 q^{72} - 86 q^{73} + 38 q^{74} - 196 q^{75} + 20 q^{76} - 64 q^{77} + 56 q^{78} - 80 q^{79} + 6 q^{80} - 219 q^{81} - 76 q^{83} + 32 q^{84} - 232 q^{85} + 44 q^{86} - 40 q^{87} + 12 q^{88} - 70 q^{89} + 78 q^{90} - 208 q^{91} + 24 q^{92} - 32 q^{93} + 48 q^{94} - 40 q^{95} + 4 q^{96} - 62 q^{97} + 57 q^{98} + 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3362))\)

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
3362.2.a \(\chi_{3362}(1, \cdot)\) 3362.2.a.a 1 1
3362.2.a.b 1
3362.2.a.c 1
3362.2.a.d 2
3362.2.a.e 2
3362.2.a.f 2
3362.2.a.g 2
3362.2.a.h 2
3362.2.a.i 2
3362.2.a.j 2
3362.2.a.k 2
3362.2.a.l 2
3362.2.a.m 2
3362.2.a.n 2
3362.2.a.o 2
3362.2.a.p 2
3362.2.a.q 3
3362.2.a.r 3
3362.2.a.s 3
3362.2.a.t 3
3362.2.a.u 4
3362.2.a.v 4
3362.2.a.w 8
3362.2.a.x 8
3362.2.a.y 8
3362.2.a.z 12
3362.2.a.ba 12
3362.2.a.bb 12
3362.2.a.bc 12
3362.2.a.bd 16
3362.2.b \(\chi_{3362}(3361, \cdot)\) n/a 136 1
3362.2.c \(\chi_{3362}(1303, \cdot)\) n/a 274 2
3362.2.d \(\chi_{3362}(51, \cdot)\) n/a 544 4
3362.2.f \(\chi_{3362}(761, \cdot)\) n/a 544 4
3362.2.g \(\chi_{3362}(207, \cdot)\) n/a 1096 8
3362.2.i \(\chi_{3362}(83, \cdot)\) n/a 5760 40
3362.2.j \(\chi_{3362}(81, \cdot)\) n/a 5760 40
3362.2.k \(\chi_{3362}(9, \cdot)\) n/a 11440 80
3362.2.l \(\chi_{3362}(37, \cdot)\) n/a 23040 160
3362.2.n \(\chi_{3362}(23, \cdot)\) n/a 23040 160
3362.2.o \(\chi_{3362}(5, \cdot)\) n/a 45760 320

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3362))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3362)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1681))\)\(^{\oplus 2}\)