Properties

Label 1656.2.u
Level $1656$
Weight $2$
Character orbit 1656.u
Rep. character $\chi_{1656}(137,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $144$
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.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 207 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 592 144 448
Cusp forms 560 144 416
Eisenstein series 32 0 32

Trace form

\( 144 q - 4 q^{9} + O(q^{10}) \) \( 144 q - 4 q^{9} - 12 q^{23} - 72 q^{25} - 24 q^{27} + 36 q^{29} + 20 q^{39} - 12 q^{41} + 84 q^{49} - 26 q^{69} - 8 q^{75} + 72 q^{77} - 36 q^{81} + 88 q^{87} - 96 q^{93} + 60 q^{95} + O(q^{100}) \)

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

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