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Properties

Label 1716.2.co
Level $1716$
Weight $2$
Character orbit 1716.co
Rep. character $\chi_{1716}(73,\cdot)$
Character field $\Q(\zeta_{20})$
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.co (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{20})\)
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

\( 224 q - 56 q^{9} + O(q^{10}) \) \( 224 q - 56 q^{9} - 8 q^{11} + 20 q^{13} + 8 q^{15} + 40 q^{29} + 16 q^{31} + 4 q^{33} + 24 q^{37} + 40 q^{41} - 4 q^{47} + 56 q^{53} + 32 q^{55} - 36 q^{59} - 40 q^{61} - 104 q^{67} - 80 q^{71} + 60 q^{73} + 80 q^{79} - 56 q^{81} - 60 q^{83} - 80 q^{85} + 16 q^{89} + 24 q^{91} + 16 q^{93} - 76 q^{97} + 12 q^{99} + O(q^{100}) \)

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

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