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Properties

Label 3696.2.gr
Level $3696$
Weight $2$
Character orbit 3696.gr
Rep. character $\chi_{3696}(257,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1504$
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.gr (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
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 1568 4768
Cusp forms 5952 1504 4448
Eisenstein series 384 64 320

Trace form

\( 1504 q + 9 q^{3} + 12 q^{7} - 3 q^{9} + O(q^{10}) \) \( 1504 q + 9 q^{3} + 12 q^{7} - 3 q^{9} + 24 q^{15} + 18 q^{19} - 10 q^{21} + 174 q^{25} + 18 q^{31} - 12 q^{33} - 6 q^{37} + 45 q^{39} + 64 q^{43} - 24 q^{45} - 4 q^{49} - 21 q^{51} - 18 q^{61} + 20 q^{63} - 16 q^{67} - 18 q^{73} + 39 q^{75} - 42 q^{79} - 3 q^{81} - 16 q^{85} + 150 q^{87} + 104 q^{91} - 7 q^{93} - 14 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3696, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(924, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1848, [\chi])\)\(^{\oplus 2}\)