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Properties

Label 3520.2.dg
Level $3520$
Weight $2$
Character orbit 3520.dg
Rep. character $\chi_{3520}(373,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $4576$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 3520 = 2^{6} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3520.dg (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3520 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3520, [\chi])\).

Total New Old
Modular forms 4640 4640 0
Cusp forms 4576 4576 0
Eisenstein series 64 64 0

Trace form

\( 4576 q - 16 q^{3} - 16 q^{5} + O(q^{10}) \) \( 4576 q - 16 q^{3} - 16 q^{5} - 16 q^{11} - 80 q^{12} + 32 q^{14} - 16 q^{15} - 32 q^{16} - 16 q^{20} + 24 q^{22} - 16 q^{23} - 16 q^{25} - 32 q^{26} - 16 q^{27} - 64 q^{34} - 32 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{42} + 32 q^{45} - 16 q^{48} - 16 q^{53} - 8 q^{55} - 224 q^{56} - 16 q^{58} - 16 q^{60} + 80 q^{66} - 16 q^{67} - 16 q^{70} - 96 q^{71} - 16 q^{75} - 8 q^{77} - 16 q^{78} - 16 q^{80} - 32 q^{81} - 96 q^{82} - 32 q^{86} + 80 q^{88} - 32 q^{91} - 320 q^{92} + 32 q^{93} - 128 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3520, [\chi])\) into newform subspaces

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