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Properties

Label 1716.2.dd
Level $1716$
Weight $2$
Character orbit 1716.dd
Rep. character $\chi_{1716}(127,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1344$
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.dd (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 572 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 2752 1344 1408
Cusp forms 2624 1344 1280
Eisenstein series 128 0 128

Trace form

\( 1344 q - 168 q^{9} + O(q^{10}) \) \( 1344 q - 168 q^{9} - 16 q^{12} + 16 q^{14} + 20 q^{16} + 24 q^{20} + 10 q^{22} + 336 q^{25} + 52 q^{26} - 20 q^{30} + 60 q^{38} + 12 q^{42} - 16 q^{48} - 144 q^{49} - 50 q^{52} - 32 q^{53} - 64 q^{56} - 36 q^{58} + 72 q^{64} + 8 q^{66} + 100 q^{74} - 64 q^{77} - 16 q^{78} + 168 q^{81} + 18 q^{82} + 20 q^{88} - 48 q^{89} - 40 q^{90} - 60 q^{92} + 24 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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