Properties

Label 920.2.f
Level $920$
Weight $2$
Character orbit 920.f
Rep. character $\chi_{920}(461,\cdot)$
Character field $\Q$
Dimension $88$
Newform subspaces $4$
Sturm bound $288$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
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 148 88 60
Cusp forms 140 88 52
Eisenstein series 8 0 8

Trace form

\( 88q - 6q^{6} + 6q^{8} - 88q^{9} + O(q^{10}) \) \( 88q - 6q^{6} + 6q^{8} - 88q^{9} + 14q^{12} + 12q^{14} + 8q^{16} - 14q^{18} - 8q^{20} - 24q^{22} + 12q^{23} - 12q^{24} - 88q^{25} - 2q^{26} - 24q^{28} + 16q^{30} - 40q^{32} - 16q^{33} + 12q^{34} + 10q^{36} + 20q^{38} - 24q^{39} + 16q^{41} + 48q^{42} - 16q^{44} - 40q^{47} + 50q^{48} + 120q^{49} + 14q^{52} - 18q^{54} + 16q^{55} + 8q^{56} - 16q^{57} - 46q^{58} - 28q^{60} - 2q^{62} + 80q^{63} - 18q^{64} - 12q^{66} + 48q^{68} + 16q^{70} - 32q^{71} + 26q^{72} - 32q^{73} + 8q^{74} + 92q^{76} + 10q^{78} - 16q^{80} + 72q^{81} - 58q^{82} + 8q^{84} + 56q^{86} + 72q^{87} - 60q^{88} - 36q^{90} + 18q^{94} - 32q^{95} - 58q^{96} + 32q^{97} + 16q^{98} + O(q^{100}) \)

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.f.a \(2\) \(7.346\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(1+i)q^{2}+2iq^{4}+iq^{5}+(-2+2i)q^{8}+\cdots\)
920.2.f.b \(8\) \(7.346\) 8.0.1871773696.1 None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{6}q^{2}+(\beta _{1}+\beta _{3})q^{3}-2q^{4}-\beta _{1}q^{5}+\cdots\)
920.2.f.c \(30\) \(7.346\) None \(0\) \(0\) \(0\) \(-4\)
920.2.f.d \(48\) \(7.346\) None \(-2\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(920, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 2}\)