Properties

Label 1716.2.bh
Level $1716$
Weight $2$
Character orbit 1716.bh
Rep. character $\chi_{1716}(43,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $336$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1716.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 572 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1716, [\chi])\).

Total New Old
Modular forms 688 336 352
Cusp forms 656 336 320
Eisenstein series 32 0 32

Trace form

\( 336 q + 168 q^{9} + O(q^{10}) \) \( 336 q + 168 q^{9} + 16 q^{12} - 16 q^{14} - 24 q^{20} + 20 q^{22} - 336 q^{25} + 48 q^{26} + 40 q^{38} - 12 q^{42} + 16 q^{48} + 184 q^{49} + 32 q^{53} - 16 q^{56} - 84 q^{58} - 72 q^{64} - 8 q^{66} - 16 q^{77} - 44 q^{78} - 168 q^{81} + 12 q^{82} - 72 q^{89} - 40 q^{92} - 24 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1716, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1716, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1716, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(572, [\chi])\)\(^{\oplus 2}\)