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Properties

Label 3640.2.ki
Level $3640$
Weight $2$
Character orbit 3640.ki
Rep. character $\chi_{3640}(173,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2656$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3640.ki (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3640 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3640, [\chi])\).

Total New Old
Modular forms 2720 2720 0
Cusp forms 2656 2656 0
Eisenstein series 64 64 0

Trace form

\( 2656 q - 6 q^{2} - 12 q^{7} + O(q^{10}) \) \( 2656 q - 6 q^{2} - 12 q^{7} - 12 q^{12} - 24 q^{15} - 4 q^{16} - 12 q^{17} + 6 q^{18} + 24 q^{20} - 12 q^{22} + 4 q^{23} - 8 q^{25} - 12 q^{26} - 6 q^{28} + 16 q^{30} - 6 q^{32} - 24 q^{33} + 24 q^{36} - 12 q^{38} - 72 q^{40} + 16 q^{42} - 12 q^{46} - 36 q^{48} + 42 q^{50} - 60 q^{52} - 60 q^{55} - 20 q^{56} - 24 q^{60} - 12 q^{62} - 48 q^{63} - 4 q^{65} - 96 q^{66} - 6 q^{68} - 114 q^{70} - 48 q^{71} + 58 q^{78} - 12 q^{80} - 2416 q^{81} + 108 q^{86} + 60 q^{87} + 12 q^{88} - 72 q^{92} - 36 q^{95} + 108 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3640, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.