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Properties

Label 3696.2.ev
Level $3696$
Weight $2$
Character orbit 3696.ev
Rep. character $\chi_{3696}(131,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $3040$
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.ev (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3696 \)
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 3104 0
Cusp forms 3040 3040 0
Eisenstein series 64 64 0

Trace form

\( 3040 q - 12 q^{3} - 8 q^{4} + O(q^{10}) \) \( 3040 q - 12 q^{3} - 8 q^{4} - 12 q^{12} - 40 q^{16} + 8 q^{22} - 12 q^{33} - 48 q^{36} - 8 q^{37} - 36 q^{42} - 12 q^{45} - 32 q^{49} + 24 q^{58} + 68 q^{60} - 128 q^{64} - 6 q^{66} + 56 q^{67} + 40 q^{70} - 72 q^{75} - 8 q^{81} - 72 q^{82} - 20 q^{88} - 80 q^{91} + 20 q^{93} + 28 q^{99} + O(q^{100}) \)

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.