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Properties

Label 3520.2.bi
Level $3520$
Weight $2$
Character orbit 3520.bi
Rep. character $\chi_{3520}(879,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $280$
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.bi (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 880 \)
Character field: \(\Q(i)\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 1184 296 888
Cusp forms 1120 280 840
Eisenstein series 64 16 48

Trace form

\( 280 q - 4 q^{5} + O(q^{10}) \) \( 280 q - 4 q^{5} + 4 q^{11} + 4 q^{45} + 216 q^{49} - 28 q^{55} - 8 q^{59} + 16 q^{69} + 48 q^{71} + 48 q^{75} - 232 q^{81} + 80 q^{91} - 76 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(880, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1760, [\chi])\)\(^{\oplus 2}\)