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Properties

Label 3696.2.dm
Level $3696$
Weight $2$
Character orbit 3696.dm
Rep. character $\chi_{3696}(2225,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $752$
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.dm (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 3168 784 2384
Cusp forms 2976 752 2224
Eisenstein series 192 32 160

Trace form

\( 752 q + 6 q^{7} - 6 q^{9} + O(q^{10}) \) \( 752 q + 6 q^{7} - 6 q^{9} - 6 q^{15} - 14 q^{21} - 168 q^{25} - 12 q^{37} - 18 q^{39} + 32 q^{43} - 14 q^{49} + 30 q^{51} - 18 q^{57} - 11 q^{63} + 64 q^{67} + 60 q^{79} - 6 q^{81} + 52 q^{85} - 2 q^{91} - 50 q^{93} + 74 q^{99} + O(q^{100}) \)

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

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