Properties

Label 120.2.k
Level $120$
Weight $2$
Character orbit 120.k
Rep. character $\chi_{120}(61,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $48$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 120.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(120, [\chi])\).

Total New Old
Modular forms 28 8 20
Cusp forms 20 8 12
Eisenstein series 8 0 8

Trace form

\( 8q + 4q^{2} - 2q^{4} + 2q^{6} + 8q^{7} + 4q^{8} - 8q^{9} + O(q^{10}) \) \( 8q + 4q^{2} - 2q^{4} + 2q^{6} + 8q^{7} + 4q^{8} - 8q^{9} - 2q^{10} - 12q^{14} - 4q^{15} + 2q^{16} - 4q^{18} - 8q^{20} - 12q^{22} - 16q^{23} + 10q^{24} - 8q^{25} + 28q^{26} - 28q^{28} + 8q^{31} + 4q^{32} + 2q^{36} + 2q^{40} + 12q^{42} + 12q^{44} - 28q^{46} + 16q^{48} + 24q^{49} - 4q^{50} - 8q^{52} - 2q^{54} + 16q^{55} - 4q^{56} - 16q^{57} - 12q^{58} + 2q^{60} + 24q^{62} - 8q^{63} + 22q^{64} + 4q^{66} - 16q^{68} + 4q^{70} - 16q^{71} - 4q^{72} - 16q^{73} + 20q^{74} + 28q^{76} + 8q^{78} + 8q^{79} + 16q^{80} + 8q^{81} + 48q^{82} - 12q^{84} - 24q^{86} + 24q^{87} + 28q^{88} + 2q^{90} - 24q^{92} - 4q^{94} - 18q^{96} + 16q^{97} - 12q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(120, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
120.2.k.a \(2\) \(0.958\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(4\) \(q+(1+i)q^{2}-iq^{3}+2iq^{4}+iq^{5}+\cdots\)
120.2.k.b \(6\) \(0.958\) 6.0.399424.1 None \(2\) \(0\) \(0\) \(4\) \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(\beta _{1}+\beta _{5})q^{4}+\beta _{1}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(120, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)