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Properties

Label 1656.2.bw
Level $1656$
Weight $2$
Character orbit 1656.bw
Rep. character $\chi_{1656}(25,\cdot)$
Character field $\Q(\zeta_{33})$
Dimension $1440$
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.bw (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 207 \)
Character field: \(\Q(\zeta_{33})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 5920 1440 4480
Cusp forms 5600 1440 4160
Eisenstein series 320 0 320

Trace form

\( 1440 q - 4 q^{5} - 4 q^{9} + O(q^{10}) \) \( 1440 q - 4 q^{5} - 4 q^{9} + 12 q^{11} + 28 q^{15} + 16 q^{17} + 24 q^{21} + 4 q^{23} + 72 q^{25} - 24 q^{27} - 12 q^{29} - 8 q^{33} - 20 q^{39} + 4 q^{41} - 12 q^{45} + 18 q^{49} + 32 q^{53} + 48 q^{57} + 12 q^{61} + 16 q^{63} - 40 q^{65} - 22 q^{69} - 74 q^{75} - 24 q^{77} + 252 q^{81} + 56 q^{83} - 134 q^{87} + 48 q^{89} + 48 q^{93} + 4 q^{95} + 364 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1656, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(414, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(828, [\chi])\)\(^{\oplus 2}\)