Properties

Label 3696.2.gp
Level $3696$
Weight $2$
Character orbit 3696.gp
Rep. character $\chi_{3696}(79,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $768$
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.gp (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 308 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 6336 768 5568
Cusp forms 5952 768 5184
Eisenstein series 384 0 384

Trace form

\( 768 q - 96 q^{9} + O(q^{10}) \) \( 768 q - 96 q^{9} + 120 q^{25} + 12 q^{33} - 240 q^{41} + 168 q^{49} + 48 q^{53} + 120 q^{73} + 72 q^{77} + 96 q^{81} - 240 q^{85} + 96 q^{89} + 72 q^{93} + 48 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3696, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(308, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(924, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1232, [\chi])\)\(^{\oplus 2}\)