↑

Properties

Label 3332.2.cb
Level $3332$
Weight $2$
Character orbit 3332.cb
Rep. character $\chi_{3332}(103,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $5376$
Sturm bound $1008$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3332.cb (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 196 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 6096 5376 720
Cusp forms 6000 5376 624
Eisenstein series 96 0 96

Trace form

\( 5376 q - 12 q^{8} + 448 q^{9} + O(q^{10}) \) \( 5376 q - 12 q^{8} + 448 q^{9} + 18 q^{10} + 6 q^{14} + 8 q^{21} - 440 q^{25} + 6 q^{28} - 40 q^{29} + 24 q^{33} - 40 q^{36} + 64 q^{37} + 42 q^{38} + 60 q^{40} + 44 q^{42} + 22 q^{44} - 24 q^{45} + 20 q^{46} - 228 q^{50} - 54 q^{52} - 84 q^{54} - 110 q^{56} - 48 q^{57} - 204 q^{60} + 56 q^{61} - 12 q^{64} - 8 q^{65} + 312 q^{66} - 56 q^{69} - 66 q^{70} + 218 q^{72} + 72 q^{73} - 28 q^{74} + 210 q^{76} + 16 q^{77} + 176 q^{78} - 168 q^{80} + 768 q^{81} - 80 q^{82} - 390 q^{84} - 50 q^{86} + 14 q^{88} + 120 q^{89} - 532 q^{90} - 72 q^{92} - 234 q^{94} + 108 q^{96} - 196 q^{98} + O(q^{100}) \)

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

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