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Properties

Label 1716.2.cf
Level $1716$
Weight $2$
Character orbit 1716.cf
Rep. character $\chi_{1716}(89,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $184$
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.cf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
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 1392 184 1208
Cusp forms 1296 184 1112
Eisenstein series 96 0 96

Trace form

\( 184 q + 4 q^{7} + O(q^{10}) \) \( 184 q + 4 q^{7} + 16 q^{13} - 16 q^{15} - 12 q^{19} + 48 q^{27} + 36 q^{31} - 4 q^{37} + 16 q^{39} + 84 q^{43} - 4 q^{45} + 36 q^{49} - 48 q^{57} + 16 q^{61} - 112 q^{63} + 32 q^{67} - 156 q^{69} - 20 q^{73} - 60 q^{75} - 32 q^{79} - 16 q^{81} - 88 q^{85} - 28 q^{91} - 44 q^{93} - 92 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1716, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(429, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(858, [\chi])\)\(^{\oplus 2}\)