Properties

Label 60.7.l
Level $60$
Weight $7$
Character orbit 60.l
Rep. character $\chi_{60}(23,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $136$
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.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 60 \)
Character field: \(\Q(i)\)
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 152 152 0
Cusp forms 136 136 0
Eisenstein series 16 16 0

Trace form

\( 136q - 4q^{6} + O(q^{10}) \) \( 136q - 4q^{6} - 2092q^{10} - 1460q^{12} - 8q^{13} - 932q^{16} - 12744q^{18} - 16056q^{21} + 25444q^{22} - 8q^{25} - 52244q^{28} + 82868q^{30} - 2920q^{33} - 69524q^{36} - 113000q^{37} + 99944q^{40} + 19436q^{42} - 62504q^{45} + 145936q^{46} - 82364q^{48} + 219504q^{52} - 286152q^{57} - 351260q^{58} + 466756q^{60} + 652976q^{61} - 61800q^{66} + 243868q^{70} - 145560q^{72} - 316856q^{73} + 269024q^{76} + 613272q^{78} + 1472232q^{81} - 1652880q^{82} - 1466984q^{85} - 1084100q^{88} + 448368q^{90} - 2869552q^{93} - 278860q^{96} + 2135272q^{97} + O(q^{100}) \)

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.l.a \(136\) \(13.803\) None \(0\) \(0\) \(0\) \(0\)