↑

Properties

Label 3696.2.ez
Level $3696$
Weight $2$
Character orbit 3696.ez
Rep. character $\chi_{3696}(421,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2304$
Sturm bound $1536$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3696 = 2^{4} \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3696.ez (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 176 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1536\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3696, [\chi])\).

Total New Old
Modular forms 6208 2304 3904
Cusp forms 6080 2304 3776
Eisenstein series 128 0 128

Trace form

\( 2304 q - 8 q^{4} + O(q^{10}) \) \( 2304 q - 8 q^{4} - 8 q^{11} + 32 q^{12} + 12 q^{14} + 8 q^{16} - 12 q^{18} + 20 q^{22} - 120 q^{26} - 32 q^{29} + 48 q^{30} + 80 q^{34} + 48 q^{37} - 112 q^{38} + 80 q^{40} - 48 q^{43} - 52 q^{44} + 64 q^{46} + 576 q^{49} - 136 q^{50} + 112 q^{52} - 48 q^{53} + 56 q^{56} - 8 q^{58} + 24 q^{60} + 16 q^{63} - 56 q^{64} + 16 q^{67} + 112 q^{68} + 24 q^{70} + 12 q^{72} + 176 q^{74} - 96 q^{75} + 256 q^{76} + 16 q^{77} + 96 q^{78} - 160 q^{79} + 80 q^{80} + 576 q^{81} + 200 q^{82} + 240 q^{83} + 12 q^{86} + 60 q^{88} + 48 q^{90} + 20 q^{92} - 168 q^{94} + 120 q^{96} + 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3696, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3696, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3696, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1232, [\chi])\)\(^{\oplus 2}\)