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Properties

Label 120.2.v
Level $120$
Weight $2$
Character orbit 120.v
Rep. character $\chi_{120}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $24$
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.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
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 56 24 32
Cusp forms 40 24 16
Eisenstein series 16 0 16

Trace form

\( 24 q + 4 q^{6} - 12 q^{8} + O(q^{10}) \) \( 24 q + 4 q^{6} - 12 q^{8} + 8 q^{10} - 8 q^{12} - 20 q^{16} + 8 q^{17} - 20 q^{20} - 28 q^{22} - 8 q^{25} - 16 q^{26} + 4 q^{28} + 8 q^{30} + 20 q^{32} - 48 q^{35} + 4 q^{36} + 40 q^{38} + 8 q^{40} + 20 q^{42} - 32 q^{43} + 48 q^{46} + 16 q^{48} + 56 q^{50} - 16 q^{51} - 48 q^{52} - 32 q^{56} - 12 q^{58} + 20 q^{60} - 16 q^{62} - 8 q^{65} - 24 q^{66} + 48 q^{67} + 72 q^{68} + 4 q^{70} + 12 q^{72} - 40 q^{73} + 48 q^{76} - 24 q^{78} + 76 q^{80} - 24 q^{81} + 24 q^{82} + 80 q^{83} - 32 q^{86} + 12 q^{88} - 12 q^{90} + 64 q^{91} + 16 q^{92} - 44 q^{96} - 24 q^{97} - 88 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
120.2.v.a 120.v 40.k $24$ $0.958$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

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