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Properties

Label 1656.2.n
Level $1656$
Weight $2$
Character orbit 1656.n
Rep. character $\chi_{1656}(91,\cdot)$
Character field $\Q$
Dimension $118$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1656 = 2^{3} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1656.n (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 184 \)
Character field: \(\Q\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1656, [\chi])\).

Total New Old
Modular forms 296 122 174
Cusp forms 280 118 162
Eisenstein series 16 4 12

Trace form

\( 118 q + 4 q^{2} + 7 q^{8} + O(q^{10}) \) \( 118 q + 4 q^{2} + 7 q^{8} + 106 q^{25} + q^{26} + 4 q^{32} + 24 q^{35} + 4 q^{41} + 102 q^{49} + 32 q^{50} + 69 q^{52} - 7 q^{58} + 16 q^{59} + 35 q^{62} - 21 q^{64} - 84 q^{70} - 4 q^{73} + 49 q^{82} - 40 q^{92} - 9 q^{94} + 64 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1656, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1656, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1656, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 3}\)