Properties

Label 920.2.e
Level $920$
Weight $2$
Character orbit 920.e
Rep. character $\chi_{920}(369,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $3$
Sturm bound $288$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(288\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 152 32 120
Cusp forms 136 32 104
Eisenstein series 16 0 16

Trace form

\( 32q + 4q^{5} - 28q^{9} + O(q^{10}) \) \( 32q + 4q^{5} - 28q^{9} + 4q^{15} + 4q^{25} - 4q^{29} - 8q^{31} + 12q^{35} + 24q^{39} - 16q^{45} - 48q^{49} - 24q^{51} - 8q^{55} - 60q^{59} + 40q^{61} - 20q^{65} + 8q^{69} - 24q^{71} + 48q^{75} + 72q^{79} + 16q^{81} - 12q^{85} - 24q^{89} - 48q^{91} + 24q^{95} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
920.2.e.a \(2\) \(7.346\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+2iq^{3}+(2-i)q^{5}-3iq^{7}-q^{9}+\cdots\)
920.2.e.b \(14\) \(7.346\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{8}q^{3}+\beta _{3}q^{5}+(\beta _{7}-\beta _{13})q^{7}+(1+\cdots)q^{9}+\cdots\)
920.2.e.c \(16\) \(7.346\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) \(q-\beta _{5}q^{3}-\beta _{7}q^{5}+(-\beta _{2}+\beta _{13})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(920, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 2}\)