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Properties

Label 1716.2.ca
Level $1716$
Weight $2$
Character orbit 1716.ca
Rep. character $\chi_{1716}(365,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $192$
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.ca (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
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 1392 192 1200
Cusp forms 1296 192 1104
Eisenstein series 96 0 96

Trace form

\( 192 q - 2 q^{3} + 2 q^{9} + O(q^{10}) \) \( 192 q - 2 q^{3} + 2 q^{9} - 6 q^{15} + 60 q^{19} + 68 q^{25} + 10 q^{27} + 36 q^{31} + 16 q^{33} + 48 q^{37} - 8 q^{45} + 24 q^{49} - 10 q^{51} - 76 q^{55} - 70 q^{57} - 60 q^{61} - 30 q^{63} - 8 q^{67} - 40 q^{69} - 20 q^{73} - 78 q^{75} - 46 q^{81} + 120 q^{85} + 8 q^{91} - 48 q^{93} + 8 q^{97} + 106 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1716, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 2}\)