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Properties

Label 1911.2.ct
Level $1911$
Weight $2$
Character orbit 1911.ct
Rep. character $\chi_{1911}(235,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1344$
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.ct (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
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 1344 1848
Cusp forms 3096 1344 1752
Eisenstein series 96 0 96

Trace form

\( 1344 q + 112 q^{4} + 4 q^{5} + 8 q^{6} - 8 q^{7} - 24 q^{8} + 112 q^{9} + O(q^{10}) \) \( 1344 q + 112 q^{4} + 4 q^{5} + 8 q^{6} - 8 q^{7} - 24 q^{8} + 112 q^{9} + 16 q^{10} + 32 q^{11} + 8 q^{13} - 16 q^{14} + 20 q^{15} + 112 q^{16} + 24 q^{17} + 96 q^{19} + 128 q^{20} + 12 q^{22} + 16 q^{23} - 12 q^{24} + 128 q^{25} + 40 q^{28} - 24 q^{29} + 16 q^{30} + 156 q^{31} + 192 q^{32} + 4 q^{33} + 96 q^{34} - 20 q^{35} - 224 q^{36} + 8 q^{37} - 24 q^{38} - 52 q^{40} - 80 q^{41} - 100 q^{42} - 40 q^{43} + 16 q^{44} - 52 q^{45} - 76 q^{47} - 32 q^{48} - 68 q^{49} - 56 q^{50} - 52 q^{51} - 12 q^{52} - 92 q^{53} - 4 q^{54} - 44 q^{55} + 20 q^{56} - 28 q^{58} - 104 q^{59} - 156 q^{60} + 8 q^{61} - 96 q^{62} + 4 q^{63} - 296 q^{64} + 24 q^{66} + 32 q^{67} - 32 q^{68} - 24 q^{69} + 4 q^{70} - 16 q^{71} + 96 q^{72} - 36 q^{73} + 60 q^{74} + 180 q^{76} - 60 q^{77} + 20 q^{79} - 168 q^{80} + 112 q^{81} - 132 q^{83} - 16 q^{84} - 104 q^{85} - 392 q^{86} + 32 q^{87} - 468 q^{88} - 140 q^{89} - 32 q^{90} + 8 q^{91} - 24 q^{92} + 148 q^{94} + 28 q^{95} - 28 q^{96} - 288 q^{97} + 36 q^{98} - 8 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1911, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 2}\)