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Properties

Label 1911.2.bh
Level $1911$
Weight $2$
Character orbit 1911.bh
Rep. character $\chi_{1911}(521,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $320$
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.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
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 556 320 236
Cusp forms 492 320 172
Eisenstein series 64 0 64

Trace form

\( 320 q + 160 q^{4} + 4 q^{9} + O(q^{10}) \) \( 320 q + 160 q^{4} + 4 q^{9} + 12 q^{10} + 30 q^{12} - 12 q^{15} - 192 q^{16} + 10 q^{18} + 24 q^{22} - 36 q^{24} - 164 q^{25} + 42 q^{30} - 12 q^{31} - 76 q^{36} + 8 q^{37} + 36 q^{40} + 32 q^{43} + 6 q^{45} + 72 q^{46} + 24 q^{51} + 54 q^{54} - 8 q^{57} + 28 q^{58} - 36 q^{60} + 72 q^{61} - 400 q^{64} + 78 q^{66} - 64 q^{67} - 82 q^{72} - 48 q^{73} - 48 q^{75} + 20 q^{78} + 96 q^{79} - 36 q^{81} - 72 q^{82} - 96 q^{85} - 60 q^{87} - 52 q^{88} + 46 q^{93} - 72 q^{94} - 66 q^{96} - 124 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1911, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)