↑

Properties

Label 3332.2.cf
Level $3332$
Weight $2$
Character orbit 3332.cf
Rep. character $\chi_{3332}(129,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $960$
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.cf (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 119 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 8448 960 7488
Cusp forms 7680 960 6720
Eisenstein series 768 0 768

Trace form

\( 960 q + O(q^{10}) \) \( 960 q - 8 q^{11} - 48 q^{15} - 8 q^{25} + 32 q^{37} + 32 q^{39} - 64 q^{51} + 64 q^{53} + 48 q^{61} - 32 q^{65} + 32 q^{71} - 120 q^{73} + 144 q^{75} - 96 q^{81} + 224 q^{85} - 144 q^{87} - 128 q^{93} - 64 q^{95} - 240 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3332, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(476, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(833, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1666, [\chi])\)\(^{\oplus 2}\)