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Properties

Label 3332.2.bf
Level $3332$
Weight $2$
Character orbit 3332.bf
Rep. character $\chi_{3332}(307,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $2688$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3332.bf (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 196 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3332, [\chi])\).

Total New Old
Modular forms 3048 2688 360
Cusp forms 3000 2688 312
Eisenstein series 48 0 48

Trace form

\( 2688 q + 12 q^{8} - 448 q^{9} + O(q^{10}) \) \( 2688 q + 12 q^{8} - 448 q^{9} - 6 q^{14} + 16 q^{21} + 464 q^{25} - 6 q^{28} + 40 q^{29} + 40 q^{36} - 40 q^{37} + 22 q^{42} + 44 q^{44} + 40 q^{46} - 24 q^{49} + 228 q^{50} + 110 q^{56} + 48 q^{57} + 180 q^{60} - 56 q^{61} + 12 q^{64} - 16 q^{65} - 336 q^{66} + 56 q^{69} + 156 q^{70} - 194 q^{72} - 56 q^{74} - 210 q^{76} + 8 q^{77} - 176 q^{78} - 648 q^{81} + 140 q^{82} - 114 q^{84} - 58 q^{86} - 14 q^{88} - 266 q^{90} + 114 q^{92} - 126 q^{94} - 252 q^{96} - 122 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3332, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3332, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3332, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)