Properties

Label 120.2.f
Level $120$
Weight $2$
Character orbit 120.f
Rep. character $\chi_{120}(49,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 120.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 32 2 30
Cusp forms 16 2 14
Eisenstein series 16 0 16

Trace form

\( 2q + 4q^{5} - 2q^{9} + O(q^{10}) \) \( 2q + 4q^{5} - 2q^{9} + 4q^{11} + 2q^{15} - 16q^{19} - 4q^{21} + 6q^{25} - 16q^{29} + 4q^{35} - 4q^{39} + 4q^{41} - 4q^{45} + 6q^{49} + 12q^{51} + 8q^{55} + 12q^{59} + 4q^{61} + 4q^{65} + 8q^{69} - 8q^{71} + 8q^{75} + 16q^{79} + 2q^{81} - 12q^{85} - 12q^{89} - 8q^{91} - 32q^{95} - 4q^{99} + O(q^{100}) \)

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.f.a \(2\) \(0.958\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{3}+(2-i)q^{5}+2iq^{7}-q^{9}+2q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)