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Properties

Label 3696.2.ff
Level $3696$
Weight $2$
Character orbit 3696.ff
Rep. character $\chi_{3696}(125,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $6080$
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.ff (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3696 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 6208 6208 0
Cusp forms 6080 6080 0
Eisenstein series 128 128 0

Trace form

\( 6080 q - 24 q^{4} + O(q^{10}) \) \( 6080 q - 24 q^{4} - 24 q^{15} - 56 q^{16} + 4 q^{18} - 4 q^{21} + 64 q^{22} - 20 q^{28} - 28 q^{30} - 44 q^{36} - 24 q^{37} + 38 q^{42} - 64 q^{43} - 72 q^{46} - 24 q^{49} + 12 q^{51} - 56 q^{58} - 148 q^{60} - 68 q^{63} - 168 q^{64} - 128 q^{67} - 96 q^{70} + 52 q^{72} - 16 q^{78} - 48 q^{79} - 24 q^{81} - 60 q^{84} + 56 q^{85} - 16 q^{88} + 116 q^{91} - 36 q^{93} + 20 q^{99} + O(q^{100}) \)

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.