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Properties

Label 1656.2.q
Level $1656$
Weight $2$
Character orbit 1656.q
Rep. character $\chi_{1656}(553,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $132$
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.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 592 132 460
Cusp forms 560 132 428
Eisenstein series 32 0 32

Trace form

\( 132 q - 2 q^{3} + 6 q^{9} + O(q^{10}) \) \( 132 q - 2 q^{3} + 6 q^{9} + 2 q^{11} + 12 q^{17} - 12 q^{19} - 66 q^{25} - 8 q^{27} - 12 q^{29} + 12 q^{31} - 18 q^{33} - 72 q^{35} - 48 q^{39} - 22 q^{41} + 18 q^{43} + 8 q^{45} - 66 q^{49} + 38 q^{51} + 24 q^{55} - 22 q^{57} + 50 q^{59} + 20 q^{63} + 12 q^{65} + 6 q^{67} + 16 q^{71} + 36 q^{73} + 46 q^{75} - 12 q^{79} - 10 q^{81} - 4 q^{83} - 24 q^{85} - 16 q^{87} - 24 q^{89} - 24 q^{91} - 28 q^{93} - 36 q^{95} - 42 q^{97} - 8 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1656, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(414, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(828, [\chi])\)\(^{\oplus 2}\)