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Properties

Label 1716.2.n
Level $1716$
Weight $2$
Character orbit 1716.n
Rep. character $\chi_{1716}(703,\cdot)$
Character field $\Q$
Dimension $144$
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.n (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 44 \)
Character field: \(\Q\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 344 144 200
Cusp forms 328 144 184
Eisenstein series 16 0 16

Trace form

\( 144 q - 8 q^{4} - 144 q^{9} + O(q^{10}) \) \( 144 q - 8 q^{4} - 144 q^{9} + 8 q^{12} + 8 q^{14} + 12 q^{22} + 128 q^{25} - 8 q^{33} + 8 q^{36} + 64 q^{37} + 56 q^{38} - 52 q^{44} + 160 q^{49} + 48 q^{53} + 56 q^{56} - 56 q^{58} - 8 q^{64} - 28 q^{66} + 136 q^{70} - 88 q^{77} - 104 q^{80} + 144 q^{81} + 96 q^{82} - 160 q^{86} - 36 q^{88} - 16 q^{92} - 32 q^{93} + 80 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1716, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(572, [\chi])\)\(^{\oplus 2}\)