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Properties

Label 2014.2
Level 2014
Weight 2
Dimension 41859
Nonzero newspaces 18
Sturm bound 505440
Trace bound 14

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Defining parameters

Level: \( N \) = \( 2014 = 2 \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(505440\)
Trace bound: \(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2014))\).

Total New Old
Modular forms 128232 41859 86373
Cusp forms 124489 41859 82630
Eisenstein series 3743 0 3743

Trace form

\( 41859 q + 3 q^{2} + 12 q^{3} + 3 q^{4} + 18 q^{5} + 12 q^{6} + 24 q^{7} + 3 q^{8} + 39 q^{9} + O(q^{10}) \) \( 41859 q + 3 q^{2} + 12 q^{3} + 3 q^{4} + 18 q^{5} + 12 q^{6} + 24 q^{7} + 3 q^{8} + 39 q^{9} + 18 q^{10} + 36 q^{11} - 6 q^{13} - 12 q^{14} + 3 q^{16} + 18 q^{17} - 15 q^{18} - 45 q^{19} - 18 q^{20} + 12 q^{21} - 18 q^{22} + 36 q^{23} + 12 q^{24} + 21 q^{25} + 6 q^{26} + 54 q^{27} + 12 q^{28} + 54 q^{29} + 72 q^{30} + 60 q^{31} + 3 q^{32} + 36 q^{33} + 54 q^{34} + 72 q^{35} + 39 q^{36} + 78 q^{37} + 39 q^{38} + 60 q^{39} - 8 q^{40} - 14 q^{41} - 112 q^{42} - 160 q^{43} + 18 q^{44} - 502 q^{45} - 104 q^{46} - 104 q^{47} - 110 q^{48} - 157 q^{49} - 285 q^{50} - 398 q^{51} - 74 q^{52} - 277 q^{53} - 300 q^{54} - 240 q^{55} - 152 q^{56} - 232 q^{57} - 216 q^{58} - 208 q^{59} - 104 q^{60} - 74 q^{61} - 116 q^{62} - 400 q^{63} - 9 q^{64} - 172 q^{65} - 208 q^{66} - 56 q^{67} + 10 q^{68} + 180 q^{69} + 72 q^{70} + 72 q^{71} + 21 q^{72} + 156 q^{73} + 114 q^{74} + 288 q^{75} + 39 q^{76} + 216 q^{77} + 96 q^{78} + 84 q^{79} + 18 q^{80} + 165 q^{81} + 54 q^{82} + 108 q^{83} - 12 q^{84} + 180 q^{85} + 60 q^{86} - 104 q^{87} + 36 q^{88} - 4 q^{89} + 54 q^{90} - 64 q^{91} - 124 q^{93} - 50 q^{95} + 12 q^{96} - 328 q^{97} + 27 q^{98} - 466 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2014))\)

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
2014.2.a \(\chi_{2014}(1, \cdot)\) 2014.2.a.a 1 1
2014.2.a.b 1
2014.2.a.c 1
2014.2.a.d 2
2014.2.a.e 6
2014.2.a.f 7
2014.2.a.g 8
2014.2.a.h 8
2014.2.a.i 9
2014.2.a.j 11
2014.2.a.k 11
2014.2.a.l 12
2014.2.b \(\chi_{2014}(1483, \cdot)\) 2014.2.b.a 2 1
2014.2.b.b 6
2014.2.b.c 30
2014.2.b.d 44
2014.2.e \(\chi_{2014}(425, \cdot)\) n/a 168 2
2014.2.f \(\chi_{2014}(189, \cdot)\) n/a 180 2
2014.2.j \(\chi_{2014}(847, \cdot)\) n/a 180 2
2014.2.k \(\chi_{2014}(213, \cdot)\) n/a 528 6
2014.2.m \(\chi_{2014}(825, \cdot)\) n/a 360 4
2014.2.n \(\chi_{2014}(77, \cdot)\) n/a 960 12
2014.2.q \(\chi_{2014}(423, \cdot)\) n/a 540 6
2014.2.t \(\chi_{2014}(115, \cdot)\) n/a 984 12
2014.2.v \(\chi_{2014}(129, \cdot)\) n/a 1080 12
2014.2.w \(\chi_{2014}(49, \cdot)\) n/a 2160 24
2014.2.y \(\chi_{2014}(75, \cdot)\) n/a 2160 24
2014.2.z \(\chi_{2014}(7, \cdot)\) n/a 2160 24
2014.2.bc \(\chi_{2014}(47, \cdot)\) n/a 6480 72
2014.2.bd \(\chi_{2014}(27, \cdot)\) n/a 4320 48
2014.2.bf \(\chi_{2014}(9, \cdot)\) n/a 6480 72
2014.2.bi \(\chi_{2014}(3, \cdot)\) n/a 12960 144

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2014))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2014)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(106))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1007))\)\(^{\oplus 2}\)