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

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

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.r.a \(4\) \(0.958\) \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(12\) \(q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
120.2.r.b \(4\) \(0.958\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(-4\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+(-1+2\zeta_{8})q^{5}+(-1+\cdots)q^{7}+\cdots\)
120.2.r.c \(4\) \(0.958\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(4\) \(-4\) \(q+(1+\zeta_{8}^{2})q^{3}+(1-2\zeta_{8})q^{5}+(-1+\cdots)q^{7}+\cdots\)

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

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