Properties

Label 120.2.r
Level $120$
Weight $2$
Character orbit 120.r
Rep. character $\chi_{120}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
Newform subspaces $3$
Sturm bound $48$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 120.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(48\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\), \(17\)

Dimensions

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

Total New Old
Modular forms 64 12 52
Cusp forms 32 12 20
Eisenstein series 32 0 32

Trace form

\( 12 q + 4 q^{7} + O(q^{10}) \) \( 12 q + 4 q^{7} + 8 q^{13} - 12 q^{15} - 16 q^{21} - 8 q^{25} - 24 q^{27} - 8 q^{31} - 12 q^{33} - 32 q^{37} + 16 q^{45} + 48 q^{51} + 28 q^{55} + 40 q^{57} + 24 q^{61} + 44 q^{63} + 40 q^{67} + 20 q^{73} - 28 q^{81} - 48 q^{85} - 20 q^{87} - 80 q^{91} - 24 q^{93} - 44 q^{97} + O(q^{100}) \)

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.r.a 120.r 15.e $4$ $0.958$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(12\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
120.2.r.b 120.r 15.e $4$ $0.958$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+(-1+2\zeta_{8})q^{5}+(-1+\cdots)q^{7}+\cdots\)
120.2.r.c 120.r 15.e $4$ $0.958$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\zeta_{8}^{2})q^{3}+(1-2\zeta_{8})q^{5}+(-1+\cdots)q^{7}+\cdots\)

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

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