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Properties

Label 60.5.l
Level $60$
Weight $5$
Character orbit 60.l
Rep. character $\chi_{60}(23,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $88$
Newform subspaces $1$
Sturm bound $60$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 5 \)
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: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(60, [\chi])\).

Total New Old
Modular forms 104 104 0
Cusp forms 88 88 0
Eisenstein series 16 16 0

Trace form

\( 88 q - 4 q^{6} + O(q^{10}) \) \( 88 q - 4 q^{6} + 148 q^{10} - 164 q^{12} - 8 q^{13} - 484 q^{16} + 456 q^{18} + 600 q^{21} - 348 q^{22} - 8 q^{25} - 148 q^{28} + 68 q^{30} - 328 q^{33} - 1556 q^{36} + 2232 q^{37} + 2024 q^{40} - 2116 q^{42} - 2504 q^{45} - 4432 q^{46} + 1540 q^{48} + 80 q^{52} + 3192 q^{57} - 1948 q^{58} + 2836 q^{60} - 7568 q^{61} + 3384 q^{66} + 8348 q^{70} + 5256 q^{72} + 5592 q^{73} - 256 q^{76} + 13176 q^{78} - 12648 q^{81} + 20400 q^{82} + 5816 q^{85} + 7932 q^{88} - 13152 q^{90} + 3680 q^{93} - 18028 q^{96} - 15208 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(60, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
60.5.l.a 60.l 60.l $88$ $6.202$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$