Properties

Label 60.7.b
Level $60$
Weight $7$
Character orbit 60.b
Rep. character $\chi_{60}(29,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $1$
Sturm bound $84$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 60.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(84\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(60, [\chi])\).

Total New Old
Modular forms 78 12 66
Cusp forms 66 12 54
Eisenstein series 12 0 12

Trace form

\( 12q + 712q^{9} + O(q^{10}) \) \( 12q + 712q^{9} + 2480q^{15} - 192q^{19} + 5348q^{21} + 18660q^{25} + 40848q^{31} - 45312q^{39} + 45340q^{45} - 242940q^{49} - 40720q^{51} - 24240q^{55} - 99312q^{61} + 108460q^{69} + 126640q^{75} + 626544q^{79} - 798268q^{81} - 732720q^{85} + 1996032q^{91} + 1632080q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(60, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
60.7.b.a \(12\) \(13.803\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+\beta _{5})q^{7}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(60, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(60, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)