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Properties

Label 1716.2.cj
Level $1716$
Weight $2$
Character orbit 1716.cj
Rep. character $\chi_{1716}(67,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $560$
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.cj (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 52 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 1376 560 816
Cusp forms 1312 560 752
Eisenstein series 64 0 64

Trace form

\( 560 q + 8 q^{5} + 280 q^{9} + O(q^{10}) \) \( 560 q + 8 q^{5} + 280 q^{9} + 32 q^{14} + 32 q^{20} - 16 q^{21} + 80 q^{26} + 80 q^{28} + 40 q^{32} + 32 q^{34} + 24 q^{37} - 80 q^{40} + 80 q^{41} - 16 q^{44} + 16 q^{45} - 40 q^{46} + 144 q^{49} - 144 q^{50} - 72 q^{52} - 16 q^{53} - 216 q^{56} + 96 q^{57} - 24 q^{58} - 56 q^{60} + 8 q^{61} + 80 q^{65} + 48 q^{68} + 152 q^{73} - 48 q^{74} - 64 q^{76} - 24 q^{78} + 8 q^{80} - 280 q^{81} - 8 q^{85} + 32 q^{86} + 72 q^{88} - 120 q^{89} - 240 q^{92} + 16 q^{93} - 64 q^{94} + 40 q^{96} - 40 q^{97} - 184 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1716, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(572, [\chi])\)\(^{\oplus 2}\)