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Properties

Label 1911.2.cr
Level $1911$
Weight $2$
Character orbit 1911.cr
Rep. character $\chi_{1911}(22,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1560$
Sturm bound $522$

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Defining parameters

Level: \( N \) \(=\) \( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1911.cr (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 637 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(522\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1911, [\chi])\).

Total New Old
Modular forms 3192 1560 1632
Cusp forms 3096 1560 1536
Eisenstein series 96 0 96

Trace form

\( 1560 q + 2 q^{3} + 128 q^{4} - q^{7} + 130 q^{9} + O(q^{10}) \) \( 1560 q + 2 q^{3} + 128 q^{4} - q^{7} + 130 q^{9} + 8 q^{10} - 8 q^{11} - 8 q^{12} + 6 q^{13} + 16 q^{14} + 108 q^{16} + 8 q^{17} - 8 q^{19} - 16 q^{20} + 10 q^{21} - 4 q^{22} - 60 q^{24} - 252 q^{25} + 16 q^{26} - 4 q^{27} + 24 q^{28} + 8 q^{29} - 12 q^{31} + 40 q^{32} + 184 q^{34} + 18 q^{35} + 128 q^{36} + 4 q^{37} + 80 q^{38} - 10 q^{39} - 8 q^{40} + 36 q^{41} - 16 q^{42} - 6 q^{43} - 200 q^{44} - 24 q^{46} - 60 q^{47} - 48 q^{48} - 41 q^{49} + 216 q^{50} + 40 q^{51} + 38 q^{52} - 48 q^{53} + 70 q^{55} + 56 q^{56} - 48 q^{57} - 72 q^{59} - 80 q^{60} + 51 q^{61} - 80 q^{62} + 6 q^{63} - 440 q^{64} + 60 q^{65} - 32 q^{66} + 38 q^{67} + 64 q^{68} + 24 q^{69} - 84 q^{70} - 172 q^{71} - 96 q^{73} + 20 q^{74} - 2 q^{75} - 32 q^{76} - 104 q^{77} - 28 q^{78} + 4 q^{79} + 40 q^{80} + 130 q^{81} - 50 q^{82} - 16 q^{83} - 14 q^{84} + 64 q^{85} - 248 q^{86} + 12 q^{87} - 84 q^{88} - 40 q^{89} - 16 q^{90} - 191 q^{91} - 72 q^{92} - 6 q^{93} + 122 q^{94} + 64 q^{95} + 280 q^{96} + 134 q^{97} - 388 q^{98} + 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1911, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1911, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1911, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 2}\)