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Properties

Label 1342.2
Level 1342
Weight 2
Dimension 18283
Nonzero newspaces 42
Sturm bound 223200
Trace bound 20

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Defining parameters

Level: \( N \) = \( 1342 = 2 \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 42 \)
Sturm bound: \(223200\)
Trace bound: \(20\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1342))\).

Total New Old
Modular forms 57000 18283 38717
Cusp forms 54601 18283 36318
Eisenstein series 2399 0 2399

Trace form

\( 18283 q + 3 q^{2} + 12 q^{3} + 3 q^{4} + 18 q^{5} + 2 q^{6} + 4 q^{7} + 3 q^{8} - q^{9} + O(q^{10}) \) \( 18283 q + 3 q^{2} + 12 q^{3} + 3 q^{4} + 18 q^{5} + 2 q^{6} + 4 q^{7} + 3 q^{8} - q^{9} - 2 q^{10} + 3 q^{11} - 8 q^{12} + 22 q^{13} + 4 q^{14} + 12 q^{15} + 3 q^{16} + 14 q^{17} + 29 q^{18} + 30 q^{19} + 18 q^{20} + 56 q^{21} + 23 q^{22} + 32 q^{23} + 2 q^{24} + 13 q^{25} + 2 q^{26} + 30 q^{27} + 4 q^{28} + 10 q^{29} + 12 q^{30} + 36 q^{31} - 7 q^{32} - 18 q^{33} + 14 q^{34} + 24 q^{35} + 29 q^{36} + 74 q^{37} + 68 q^{39} - 2 q^{40} + 46 q^{41} + 36 q^{42} + 32 q^{43} - 7 q^{44} + 134 q^{45} + 32 q^{46} - 56 q^{47} - 28 q^{48} - 229 q^{49} - 97 q^{50} - 154 q^{51} - 148 q^{52} - 58 q^{53} - 320 q^{54} - 242 q^{55} - 96 q^{56} - 410 q^{57} - 230 q^{58} - 190 q^{59} + 32 q^{60} - 467 q^{61} - 324 q^{62} - 448 q^{63} + 3 q^{64} - 188 q^{65} - 148 q^{66} - 456 q^{67} - 106 q^{68} - 412 q^{69} - 296 q^{70} - 64 q^{71} - 151 q^{72} - 138 q^{73} - 76 q^{74} - 138 q^{75} - 36 q^{77} + 88 q^{78} + 140 q^{79} - 2 q^{80} + 93 q^{81} + 56 q^{82} + 122 q^{83} + 16 q^{84} + 104 q^{85} + 2 q^{86} + 160 q^{87} + 3 q^{88} + 110 q^{89} + 54 q^{90} + 136 q^{91} + 12 q^{92} + 124 q^{93} + 24 q^{94} + 140 q^{95} + 12 q^{96} + 104 q^{97} + 81 q^{98} + 39 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1342))\)

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
1342.2.a \(\chi_{1342}(1, \cdot)\) 1342.2.a.a 1 1
1342.2.a.b 1
1342.2.a.c 1
1342.2.a.d 1
1342.2.a.e 2
1342.2.a.f 2
1342.2.a.g 3
1342.2.a.h 4
1342.2.a.i 4
1342.2.a.j 4
1342.2.a.k 5
1342.2.a.l 6
1342.2.a.m 6
1342.2.a.n 9
1342.2.c \(\chi_{1342}(243, \cdot)\) 1342.2.c.a 2 1
1342.2.c.b 8
1342.2.c.c 14
1342.2.c.d 26
1342.2.e \(\chi_{1342}(1145, \cdot)\) n/a 104 2
1342.2.f \(\chi_{1342}(1209, \cdot)\) n/a 124 2
1342.2.h \(\chi_{1342}(619, \cdot)\) n/a 248 4
1342.2.i \(\chi_{1342}(245, \cdot)\) n/a 240 4
1342.2.j \(\chi_{1342}(119, \cdot)\) n/a 248 4
1342.2.k \(\chi_{1342}(375, \cdot)\) n/a 192 4
1342.2.l \(\chi_{1342}(339, \cdot)\) n/a 248 4
1342.2.m \(\chi_{1342}(9, \cdot)\) n/a 248 4
1342.2.o \(\chi_{1342}(353, \cdot)\) n/a 108 2
1342.2.v \(\chi_{1342}(487, \cdot)\) n/a 248 4
1342.2.w \(\chi_{1342}(113, \cdot)\) n/a 248 4
1342.2.x \(\chi_{1342}(235, \cdot)\) n/a 248 4
1342.2.bb \(\chi_{1342}(529, \cdot)\) n/a 200 4
1342.2.bd \(\chi_{1342}(125, \cdot)\) n/a 248 4
1342.2.bf \(\chi_{1342}(3, \cdot)\) n/a 248 4
1342.2.bj \(\chi_{1342}(21, \cdot)\) n/a 248 4
1342.2.bk \(\chi_{1342}(25, \cdot)\) n/a 496 8
1342.2.bl \(\chi_{1342}(199, \cdot)\) n/a 416 8
1342.2.bm \(\chi_{1342}(269, \cdot)\) n/a 496 8
1342.2.bn \(\chi_{1342}(15, \cdot)\) n/a 496 8
1342.2.bo \(\chi_{1342}(47, \cdot)\) n/a 496 8
1342.2.bp \(\chi_{1342}(137, \cdot)\) n/a 496 8
1342.2.br \(\chi_{1342}(145, \cdot)\) n/a 496 8
1342.2.bt \(\chi_{1342}(85, \cdot)\) n/a 496 8
1342.2.bu \(\chi_{1342}(175, \cdot)\) n/a 496 8
1342.2.by \(\chi_{1342}(233, \cdot)\) n/a 496 8
1342.2.bz \(\chi_{1342}(557, \cdot)\) n/a 496 8
1342.2.ca \(\chi_{1342}(211, \cdot)\) n/a 496 8
1342.2.cd \(\chi_{1342}(5, \cdot)\) n/a 496 8
1342.2.cf \(\chi_{1342}(45, \cdot)\) n/a 432 8
1342.2.cj \(\chi_{1342}(141, \cdot)\) n/a 496 8
1342.2.ck \(\chi_{1342}(75, \cdot)\) n/a 496 8
1342.2.cl \(\chi_{1342}(97, \cdot)\) n/a 496 8
1342.2.ct \(\chi_{1342}(49, \cdot)\) n/a 496 8
1342.2.cu \(\chi_{1342}(7, \cdot)\) n/a 992 16
1342.2.cx \(\chi_{1342}(35, \cdot)\) n/a 992 16
1342.2.cy \(\chi_{1342}(51, \cdot)\) n/a 992 16
1342.2.cz \(\chi_{1342}(29, \cdot)\) n/a 992 16
1342.2.dd \(\chi_{1342}(43, \cdot)\) n/a 992 16
1342.2.de \(\chi_{1342}(17, \cdot)\) n/a 992 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1342))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1342)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(61))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(122))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(671))\)\(^{\oplus 2}\)