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Properties

Label 1911.2.j
Level $1911$
Weight $2$
Character orbit 1911.j
Rep. character $\chi_{1911}(373,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $186$
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.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(522\)

Dimensions

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

Total New Old
Modular forms 554 186 368
Cusp forms 490 186 304
Eisenstein series 64 0 64

Trace form

\( 186 q - 6 q^{3} - 92 q^{4} + 186 q^{9} + O(q^{10}) \) \( 186 q - 6 q^{3} - 92 q^{4} + 186 q^{9} - 16 q^{10} - 8 q^{11} + 8 q^{12} - 2 q^{13} - 82 q^{16} - 4 q^{17} - 6 q^{19} + 8 q^{20} + 2 q^{22} + 8 q^{23} + 24 q^{24} - 83 q^{25} + 2 q^{26} - 6 q^{27} + 4 q^{29} + 11 q^{31} - 20 q^{32} + 56 q^{34} - 92 q^{36} - 9 q^{37} - 24 q^{38} - 6 q^{39} + 34 q^{40} - 18 q^{41} + 10 q^{43} + 20 q^{44} + 4 q^{46} - 12 q^{47} + 18 q^{48} + 42 q^{50} - 12 q^{51} - 48 q^{52} + 20 q^{53} + 34 q^{55} + 10 q^{57} - 32 q^{58} + 32 q^{59} - 44 q^{60} - 18 q^{61} - 16 q^{62} + 212 q^{64} + 16 q^{65} + 16 q^{66} + 114 q^{67} - 32 q^{68} + 12 q^{69} + 6 q^{71} - 4 q^{73} + 28 q^{74} + 29 q^{75} + 12 q^{76} - 6 q^{78} - 5 q^{79} + 40 q^{80} + 186 q^{81} - 28 q^{82} - 64 q^{83} - 68 q^{85} - 20 q^{86} + 30 q^{87} + 48 q^{88} - 16 q^{89} - 16 q^{90} - 28 q^{92} - 11 q^{93} - 128 q^{94} + 48 q^{95} - 14 q^{96} - 23 q^{97} - 8 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1911, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 2}\)