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Properties

Label 1911.2.bz
Level $1911$
Weight $2$
Character orbit 1911.bz
Rep. character $\chi_{1911}(97,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $376$
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.bz (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(522\)

Dimensions

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

Total New Old
Modular forms 1112 376 736
Cusp forms 984 376 608
Eisenstein series 128 0 128

Trace form

\( 376 q + 188 q^{9} + O(q^{10}) \) \( 376 q + 188 q^{9} + 16 q^{11} + 200 q^{16} + 16 q^{22} + 40 q^{32} - 28 q^{37} + 20 q^{39} - 72 q^{43} + 16 q^{44} + 120 q^{46} - 96 q^{50} + 128 q^{53} - 76 q^{57} + 128 q^{58} + 128 q^{60} - 64 q^{65} + 28 q^{67} + 8 q^{71} - 64 q^{74} + 16 q^{78} - 64 q^{79} - 188 q^{81} - 40 q^{85} + 48 q^{86} - 288 q^{88} + 16 q^{92} - 40 q^{93} - 96 q^{95} - 16 q^{99} + O(q^{100}) \)

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

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