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Properties

Label 1334.2
Level 1334
Weight 2
Dimension 18369
Nonzero newspaces 12
Sturm bound 221760
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1334 = 2 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(221760\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1334))\).

Total New Old
Modular forms 56672 18369 38303
Cusp forms 54209 18369 35840
Eisenstein series 2463 0 2463

Trace form

\( 18369 q + 3 q^{2} + 12 q^{3} + 3 q^{4} + 18 q^{5} + 12 q^{6} + 24 q^{7} + 3 q^{8} + 39 q^{9} + O(q^{10}) \) \( 18369 q + 3 q^{2} + 12 q^{3} + 3 q^{4} + 18 q^{5} + 12 q^{6} + 24 q^{7} + 3 q^{8} + 39 q^{9} + 18 q^{10} + 36 q^{11} + 12 q^{12} + 42 q^{13} + 24 q^{14} + 28 q^{15} + 3 q^{16} + 10 q^{17} - 49 q^{18} + 16 q^{19} - 40 q^{20} - 148 q^{21} - 64 q^{22} - 69 q^{23} - 44 q^{24} - 107 q^{25} - 72 q^{26} - 180 q^{27} - 20 q^{28} - 75 q^{29} - 184 q^{30} - 60 q^{31} + 3 q^{32} - 68 q^{33} - 16 q^{34} - 12 q^{35} - 17 q^{36} - 30 q^{37} + 4 q^{38} - 32 q^{39} + 4 q^{40} + 82 q^{41} + 96 q^{42} + 44 q^{43} + 36 q^{44} + 32 q^{45} + 47 q^{46} + 12 q^{48} - 73 q^{49} + 93 q^{50} + 16 q^{51} + 42 q^{52} - 8 q^{53} + 76 q^{54} - 184 q^{55} - 20 q^{56} - 92 q^{57} + 15 q^{58} - 96 q^{59} + 28 q^{60} - 102 q^{61} - 36 q^{62} - 132 q^{63} + 3 q^{64} - 182 q^{65} - 32 q^{66} + 4 q^{67} - 34 q^{68} - 88 q^{69} - 88 q^{70} - 228 q^{71} - 49 q^{72} - 48 q^{73} - 230 q^{74} - 260 q^{75} - 52 q^{76} - 212 q^{77} - 188 q^{78} - 92 q^{79} - 26 q^{80} - 349 q^{81} - 74 q^{82} - 148 q^{83} - 116 q^{84} - 144 q^{85} - 192 q^{86} - 110 q^{87} + 36 q^{88} - 54 q^{89} - 46 q^{90} - 88 q^{91} - 37 q^{92} + 160 q^{93} + 32 q^{94} - 220 q^{95} + 12 q^{96} - 8 q^{97} - 141 q^{98} - 276 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1334))\)

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
1334.2.a \(\chi_{1334}(1, \cdot)\) 1334.2.a.a 1 1
1334.2.a.b 1
1334.2.a.c 1
1334.2.a.d 4
1334.2.a.e 4
1334.2.a.f 5
1334.2.a.g 5
1334.2.a.h 5
1334.2.a.i 8
1334.2.a.j 9
1334.2.a.k 10
1334.2.c \(\chi_{1334}(231, \cdot)\) 1334.2.c.a 28 1
1334.2.c.b 28
1334.2.f \(\chi_{1334}(505, \cdot)\) n/a 120 2
1334.2.g \(\chi_{1334}(139, \cdot)\) n/a 324 6
1334.2.h \(\chi_{1334}(59, \cdot)\) n/a 560 10
1334.2.j \(\chi_{1334}(93, \cdot)\) n/a 336 6
1334.2.m \(\chi_{1334}(173, \cdot)\) n/a 600 10
1334.2.o \(\chi_{1334}(137, \cdot)\) n/a 720 12
1334.2.q \(\chi_{1334}(17, \cdot)\) n/a 1200 20
1334.2.s \(\chi_{1334}(25, \cdot)\) n/a 3600 60
1334.2.u \(\chi_{1334}(9, \cdot)\) n/a 3600 60
1334.2.x \(\chi_{1334}(11, \cdot)\) n/a 7200 120

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1334))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1334)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(667))\)\(^{\oplus 2}\)