↑

Properties

Label 920.2.bb
Level $920$
Weight $2$
Character orbit 920.bb
Rep. character $\chi_{920}(11,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $960$
Newform subspaces $2$
Sturm bound $288$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.bb (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 184 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(920, [\chi])\).

Total New Old
Modular forms 1480 960 520
Cusp forms 1400 960 440
Eisenstein series 80 0 80

Trace form

\( 960 q + 4 q^{2} - 8 q^{4} + 10 q^{6} - 2 q^{8} - 96 q^{9} + 6 q^{12} - 24 q^{16} + 14 q^{18} + 4 q^{24} - 96 q^{25} + 14 q^{26} + 24 q^{27} - 16 q^{32} - 22 q^{34} + 108 q^{36} - 110 q^{38} + 88 q^{40}+ \cdots - 196 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(920, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
920.2.bb.a 920.bb 184.j $480$ $7.346$ None 920.2.bb.a \(2\) \(0\) \(-48\) \(0\) $\mathrm{SU}(2)[C_{22}]$
920.2.bb.b 920.bb 184.j $480$ $7.346$ None 920.2.bb.a \(2\) \(0\) \(48\) \(0\) $\mathrm{SU}(2)[C_{22}]$

Decomposition of \(S_{2}^{\mathrm{old}}(920, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(920, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 2}\)