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Properties

Label 2014.2.n
Level $2014$
Weight $2$
Character orbit 2014.n
Rep. character $\chi_{2014}(77,\cdot)$
Character field $\Q(\zeta_{13})$
Dimension $960$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 2014 = 2 \cdot 19 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2014.n (of order \(13\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 53 \)
Character field: \(\Q(\zeta_{13})\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2014, [\chi])\).

Total New Old
Modular forms 3288 960 2328
Cusp forms 3192 960 2232
Eisenstein series 96 0 96

Trace form

\( 960 q + 2 q^{2} + 8 q^{3} - 80 q^{4} + 12 q^{5} + 4 q^{6} + 8 q^{7} + 2 q^{8} - 68 q^{9} + O(q^{10}) \) \( 960 q + 2 q^{2} + 8 q^{3} - 80 q^{4} + 12 q^{5} + 4 q^{6} + 8 q^{7} + 2 q^{8} - 68 q^{9} + 20 q^{10} + 12 q^{11} + 8 q^{12} + 20 q^{13} - 28 q^{15} - 80 q^{16} + 20 q^{17} + 26 q^{18} + 12 q^{20} + 16 q^{21} + 8 q^{22} + 16 q^{23} + 4 q^{24} - 32 q^{25} + 28 q^{26} + 32 q^{27} + 8 q^{28} + 28 q^{29} - 32 q^{31} + 2 q^{32} + 36 q^{33} + 20 q^{34} + 56 q^{35} - 120 q^{36} + 52 q^{37} + 6 q^{38} + 52 q^{39} - 58 q^{40} - 8 q^{41} - 60 q^{42} + 44 q^{43} + 12 q^{44} - 160 q^{45} + 16 q^{46} - 44 q^{48} - 208 q^{49} - 100 q^{50} + 64 q^{51} + 20 q^{52} + 58 q^{53} - 180 q^{54} + 96 q^{55} + 4 q^{57} - 98 q^{58} - 56 q^{59} - 28 q^{60} + 32 q^{61} + 16 q^{62} - 144 q^{63} - 80 q^{64} + 24 q^{65} - 32 q^{66} + 44 q^{67} - 6 q^{68} + 96 q^{69} + 72 q^{70} + 96 q^{71} + 26 q^{72} - 60 q^{73} + 40 q^{74} - 80 q^{75} + 48 q^{77} + 80 q^{78} + 72 q^{79} + 12 q^{80} - 108 q^{81} - 124 q^{82} + 32 q^{83} + 16 q^{84} + 80 q^{85} - 160 q^{86} + 56 q^{87} + 8 q^{88} + 70 q^{89} + 76 q^{90} - 8 q^{91} + 16 q^{92} + 68 q^{93} + 16 q^{94} + 4 q^{96} - 102 q^{97} + 82 q^{98} + 132 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2014, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2014, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2014, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(53, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(106, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1007, [\chi])\)\(^{\oplus 2}\)