Properties

Label 3696.2.em
Level $3696$
Weight $2$
Character orbit 3696.em
Rep. character $\chi_{3696}(1453,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1280$
Sturm bound $1536$

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Defining parameters

Level: \( N \) \(=\) \( 3696 = 2^{4} \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3696.em (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 3104 1280 1824
Cusp forms 3040 1280 1760
Eisenstein series 64 0 64

Trace form

\( 1280 q - 48 q^{8} + O(q^{10}) \) \( 1280 q - 48 q^{8} + 24 q^{10} - 32 q^{14} + 32 q^{20} + 40 q^{28} + 96 q^{31} - 64 q^{34} + 48 q^{35} + 80 q^{38} + 104 q^{40} - 40 q^{42} + 16 q^{44} + 40 q^{46} - 64 q^{48} + 48 q^{50} + 72 q^{52} + 112 q^{56} + 24 q^{58} - 32 q^{59} + 24 q^{60} + 288 q^{62} + 48 q^{64} + 48 q^{67} + 40 q^{68} + 152 q^{70} - 48 q^{76} + 48 q^{78} - 24 q^{80} + 640 q^{81} - 40 q^{82} + 16 q^{86} - 32 q^{91} + 144 q^{92} + 96 q^{95} - 40 q^{96} - 160 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3696, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1232, [\chi])\)\(^{\oplus 2}\)