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Properties

Label 1911.2.p
Level $1911$
Weight $2$
Character orbit 1911.p
Rep. character $\chi_{1911}(538,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $184$
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.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(i)\)
Sturm bound: \(522\)

Dimensions

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

Total New Old
Modular forms 552 184 368
Cusp forms 488 184 304
Eisenstein series 64 0 64

Trace form

\( 184 q - 184 q^{9} + O(q^{10}) \) \( 184 q - 184 q^{9} - 16 q^{11} - 160 q^{16} - 16 q^{22} - 40 q^{32} - 28 q^{37} - 4 q^{39} - 16 q^{44} - 120 q^{50} + 64 q^{53} - 12 q^{57} + 16 q^{58} - 8 q^{60} - 32 q^{65} + 36 q^{67} - 8 q^{71} - 128 q^{74} - 64 q^{78} - 32 q^{79} + 184 q^{81} + 136 q^{85} - 48 q^{86} - 208 q^{92} - 12 q^{93} + 16 q^{99} + O(q^{100}) \)

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

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