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Properties

Label 1716.2.cd
Level $1716$
Weight $2$
Character orbit 1716.cd
Rep. character $\chi_{1716}(443,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1152$
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.cd (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 132 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 1376 1152 224
Cusp forms 1312 1152 160
Eisenstein series 64 0 64

Trace form

\( 1152 q + 8 q^{9} + O(q^{10}) \) \( 1152 q + 8 q^{9} - 8 q^{10} + 44 q^{16} + 20 q^{22} + 272 q^{25} + 48 q^{28} + 36 q^{33} - 10 q^{36} + 8 q^{40} - 76 q^{42} + 96 q^{45} - 32 q^{46} - 56 q^{48} + 304 q^{49} - 12 q^{52} + 12 q^{54} - 28 q^{57} - 32 q^{58} - 144 q^{60} - 72 q^{64} - 58 q^{66} + 24 q^{69} - 72 q^{70} - 134 q^{72} - 72 q^{73} - 48 q^{76} - 40 q^{78} - 40 q^{81} - 60 q^{82} - 100 q^{84} - 48 q^{85} - 152 q^{88} + 136 q^{90} + 24 q^{93} - 64 q^{94} + 160 q^{96} - 152 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1716, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 2}\)