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Properties

Label 60.6.d
Level $60$
Weight $6$
Character orbit 60.d
Rep. character $\chi_{60}(49,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 60.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(60, [\chi])\).

Total New Old
Modular forms 66 6 60
Cusp forms 54 6 48
Eisenstein series 12 0 12

Trace form

\( 6 q - 38 q^{5} - 486 q^{9} + O(q^{10}) \) \( 6 q - 38 q^{5} - 486 q^{9} + 296 q^{11} + 396 q^{15} - 6000 q^{19} + 1584 q^{21} + 6054 q^{25} - 15924 q^{29} + 264 q^{31} + 20096 q^{35} + 16340 q^{41} + 3078 q^{45} - 27654 q^{49} + 15624 q^{51} - 26088 q^{55} + 92456 q^{59} + 6252 q^{61} - 52440 q^{65} + 18936 q^{69} - 160800 q^{71} - 29448 q^{75} + 128952 q^{79} + 39366 q^{81} - 177864 q^{85} + 76060 q^{89} - 98400 q^{91} + 232800 q^{95} - 23976 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(60, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
60.6.d.a 60.d 5.b $6$ $9.623$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(-38\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-6-\beta _{1}-\beta _{2})q^{5}+(-3\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(60, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(60, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)