Properties

Label 120.2.w
Level $120$
Weight $2$
Character orbit 120.w
Rep. character $\chi_{120}(53,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $40$
Newform subspaces $3$
Sturm bound $48$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 120.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 120 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(48\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

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

Total New Old
Modular forms 56 56 0
Cusp forms 40 40 0
Eisenstein series 16 16 0

Trace form

\( 40 q - 4 q^{6} - 8 q^{7} + O(q^{10}) \) \( 40 q - 4 q^{6} - 8 q^{7} - 12 q^{10} - 8 q^{12} - 4 q^{15} - 4 q^{16} - 20 q^{18} - 20 q^{22} - 8 q^{25} + 28 q^{28} - 32 q^{30} - 32 q^{31} - 16 q^{33} + 28 q^{36} + 24 q^{40} - 32 q^{42} + 24 q^{46} + 44 q^{48} + 8 q^{52} - 48 q^{55} - 16 q^{57} + 44 q^{58} + 56 q^{60} + 24 q^{63} + 16 q^{66} + 84 q^{70} + 32 q^{72} - 8 q^{73} - 88 q^{76} + 64 q^{78} - 24 q^{81} + 64 q^{82} + 64 q^{87} - 116 q^{88} + 84 q^{90} - 52 q^{96} + 8 q^{97} + O(q^{100}) \)

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.w.a 120.w 120.w $4$ $0.958$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-6}) \) \(-4\) \(0\) \(4\) \(-4\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots\)
120.2.w.b 120.w 120.w $4$ $0.958$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-6}) \) \(4\) \(0\) \(-4\) \(-4\) $\mathrm{U}(1)[D_{4}]$ \(q+(1-\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
120.2.w.c 120.w 120.w $32$ $0.958$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$