↑

Properties

Label 3520.2.do
Level $3520$
Weight $2$
Character orbit 3520.do
Rep. character $\chi_{3520}(79,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1120$
Sturm bound $1152$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3520 = 2^{6} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3520.do (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 880 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 4736 1184 3552
Cusp forms 4480 1120 3360
Eisenstein series 256 64 192

Trace form

\( 1120 q - 6 q^{5} + O(q^{10}) \) \( 1120 q - 6 q^{5} + 16 q^{11} + 20 q^{19} - 20 q^{29} + 10 q^{35} + 40 q^{39} - 24 q^{45} - 256 q^{49} + 20 q^{51} + 48 q^{55} + 28 q^{59} - 20 q^{61} + 24 q^{69} - 8 q^{71} + 42 q^{75} + 192 q^{81} - 10 q^{85} - 60 q^{91} + 96 q^{99} + O(q^{100}) \)

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

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