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Properties

Label 1911.2.bd
Level $1911$
Weight $2$
Character orbit 1911.bd
Rep. character $\chi_{1911}(589,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $190$
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.bd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(522\)

Dimensions

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

Total New Old
Modular forms 556 190 366
Cusp forms 492 190 302
Eisenstein series 64 0 64

Trace form

\( 190 q - q^{3} + 94 q^{4} - 95 q^{9} + O(q^{10}) \) \( 190 q - q^{3} + 94 q^{4} - 95 q^{9} + 8 q^{10} + 18 q^{11} - 12 q^{12} + q^{13} + 6 q^{15} - 88 q^{16} - 8 q^{17} - 6 q^{19} - 36 q^{20} + 20 q^{22} - 2 q^{23} - 194 q^{25} - 40 q^{26} + 2 q^{27} + 10 q^{29} - 6 q^{33} + 94 q^{36} + 30 q^{37} + 56 q^{38} - 8 q^{39} + 88 q^{40} + 24 q^{41} + 9 q^{43} + 6 q^{45} + 24 q^{46} - 4 q^{48} - 180 q^{50} + 32 q^{51} + 6 q^{52} + 8 q^{53} - 24 q^{55} + 144 q^{58} + 90 q^{59} + 5 q^{61} + 4 q^{62} - 232 q^{64} - 38 q^{65} + 32 q^{66} - 63 q^{67} - 16 q^{68} + 2 q^{69} + 18 q^{71} + 16 q^{74} + 23 q^{75} - 36 q^{76} - 20 q^{78} - 130 q^{79} - 120 q^{80} - 95 q^{81} + 60 q^{82} - 30 q^{87} - 72 q^{88} - 108 q^{89} - 16 q^{90} + 128 q^{92} - 3 q^{93} + 8 q^{94} + 4 q^{95} + 69 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1911, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 2}\)