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Properties

Label 1716.2.cm
Level $1716$
Weight $2$
Character orbit 1716.cm
Rep. character $\chi_{1716}(289,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $224$
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.cm (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 2784 224 2560
Cusp forms 2592 224 2368
Eisenstein series 192 0 192

Trace form

\( 224 q + 28 q^{9} + O(q^{10}) \) \( 224 q + 28 q^{9} + 12 q^{11} - 14 q^{13} - 4 q^{15} + 8 q^{17} + 16 q^{19} - 20 q^{23} - 68 q^{25} + 12 q^{29} + 8 q^{31} - 2 q^{33} - 4 q^{35} + 24 q^{37} - 8 q^{39} + 20 q^{41} + 48 q^{43} - 92 q^{47} + 16 q^{49} + 40 q^{51} - 36 q^{53} - 16 q^{55} + 10 q^{59} - 44 q^{61} - 100 q^{65} + 64 q^{67} + 14 q^{69} - 56 q^{71} - 84 q^{73} + 8 q^{75} - 44 q^{77} - 8 q^{79} + 28 q^{81} + 104 q^{83} + 20 q^{85} + 8 q^{87} - 8 q^{89} - 62 q^{91} - 8 q^{93} + 40 q^{95} - 10 q^{97} - 4 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1716, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(286, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(429, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(572, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(858, [\chi])\)\(^{\oplus 2}\)