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Properties

Label 360.6.s
Level $360$
Weight $6$
Character orbit 360.s
Rep. character $\chi_{360}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $60$
Newform subspaces $2$
Sturm bound $432$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 360.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(432\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(360, [\chi])\).

Total New Old
Modular forms 752 60 692
Cusp forms 688 60 628
Eisenstein series 64 0 64

Trace form

\( 60 q + 152 q^{7} + O(q^{10}) \) \( 60 q + 152 q^{7} + 796 q^{13} - 5104 q^{25} + 9680 q^{31} - 14932 q^{37} - 103576 q^{55} + 86960 q^{67} - 27092 q^{73} - 158160 q^{85} - 373840 q^{91} + 177788 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(360, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
360.6.s.a 360.s 15.e $28$ $57.738$ None \(0\) \(0\) \(0\) \(296\) $\mathrm{SU}(2)[C_{4}]$
360.6.s.b 360.s 15.e $32$ $57.738$ None \(0\) \(0\) \(0\) \(-144\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{6}^{\mathrm{old}}(360, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(360, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)