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Properties

Label 1474.2
Level 1474
Weight 2
Dimension 22059
Nonzero newspaces 16
Sturm bound 269280
Trace bound 2

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Defining parameters

Level: \( N \) = \( 1474 = 2 \cdot 11 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(269280\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1474))\).

Total New Old
Modular forms 68640 22059 46581
Cusp forms 66001 22059 43942
Eisenstein series 2639 0 2639

Trace form

\( 22059 q + 3 q^{2} + 12 q^{3} + 3 q^{4} + 18 q^{5} + 2 q^{6} + 4 q^{7} + 3 q^{8} - q^{9} + O(q^{10}) \) \( 22059 q + 3 q^{2} + 12 q^{3} + 3 q^{4} + 18 q^{5} + 2 q^{6} + 4 q^{7} + 3 q^{8} - q^{9} - 2 q^{10} + 3 q^{11} - 8 q^{12} + 22 q^{13} + 4 q^{14} + 12 q^{15} + 3 q^{16} + 14 q^{17} + 29 q^{18} + 30 q^{19} + 18 q^{20} + 56 q^{21} + 23 q^{22} + 32 q^{23} + 2 q^{24} + 13 q^{25} + 2 q^{26} + 30 q^{27} + 4 q^{28} + 10 q^{29} + 12 q^{30} + 36 q^{31} - 7 q^{32} - 18 q^{33} + 14 q^{34} + 24 q^{35} + 29 q^{36} + 74 q^{37} + 68 q^{39} - 2 q^{40} + 46 q^{41} + 36 q^{42} + 32 q^{43} - 7 q^{44} + 134 q^{45} + 32 q^{46} + 64 q^{47} + 12 q^{48} + 51 q^{49} + 53 q^{50} + 86 q^{51} - 42 q^{52} - 70 q^{53} - 158 q^{54} - 200 q^{55} + 24 q^{56} - 238 q^{57} - 254 q^{58} - 214 q^{59} - 232 q^{60} - 482 q^{61} - 96 q^{62} - 500 q^{63} + 3 q^{64} - 476 q^{65} - 292 q^{66} - 219 q^{67} - 118 q^{68} - 196 q^{69} - 464 q^{70} - 472 q^{71} - q^{72} - 470 q^{73} - 58 q^{74} - 386 q^{75} - 224 q^{76} - 108 q^{77} - 176 q^{78} - 168 q^{79} - 2 q^{80} - 303 q^{81} - 142 q^{82} - 10 q^{83} - 28 q^{84} + 104 q^{85} + 2 q^{86} + 160 q^{87} + 3 q^{88} + 110 q^{89} + 54 q^{90} + 136 q^{91} + 12 q^{92} + 124 q^{93} + 24 q^{94} + 140 q^{95} + 12 q^{96} + 104 q^{97} + 81 q^{98} + 39 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1474))\)

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
1474.2.a \(\chi_{1474}(1, \cdot)\) 1474.2.a.a 1 1
1474.2.a.b 2
1474.2.a.c 5
1474.2.a.d 5
1474.2.a.e 6
1474.2.a.f 7
1474.2.a.g 7
1474.2.a.h 7
1474.2.a.i 7
1474.2.a.j 8
1474.2.c \(\chi_{1474}(1473, \cdot)\) 1474.2.c.a 34 1
1474.2.c.b 34
1474.2.e \(\chi_{1474}(573, \cdot)\) n/a 116 2
1474.2.f \(\chi_{1474}(135, \cdot)\) n/a 264 4
1474.2.g \(\chi_{1474}(373, \cdot)\) n/a 136 2
1474.2.k \(\chi_{1474}(535, \cdot)\) n/a 272 4
1474.2.m \(\chi_{1474}(89, \cdot)\) n/a 540 10
1474.2.n \(\chi_{1474}(37, \cdot)\) n/a 544 8
1474.2.p \(\chi_{1474}(43, \cdot)\) n/a 680 10
1474.2.t \(\chi_{1474}(105, \cdot)\) n/a 544 8
1474.2.u \(\chi_{1474}(23, \cdot)\) n/a 1160 20
1474.2.v \(\chi_{1474}(9, \cdot)\) n/a 2720 40
1474.2.y \(\chi_{1474}(87, \cdot)\) n/a 1360 20
1474.2.ba \(\chi_{1474}(139, \cdot)\) n/a 2720 40
1474.2.bc \(\chi_{1474}(47, \cdot)\) n/a 5440 80
1474.2.bd \(\chi_{1474}(7, \cdot)\) n/a 5440 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1474))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1474)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(134))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(737))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1474))\)\(^{\oplus 1}\)