↑

Properties

Label 120.6.r
Level $120$
Weight $6$
Character orbit 120.r
Rep. character $\chi_{120}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $60$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 120.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(120, [\chi])\).

Total New Old
Modular forms 256 60 196
Cusp forms 224 60 164
Eisenstein series 32 0 32

Trace form

\( 60 q - 76 q^{7} + O(q^{10}) \) \( 60 q - 76 q^{7} - 1592 q^{13} + 2868 q^{15} - 4480 q^{21} + 2552 q^{25} - 744 q^{27} - 4840 q^{31} + 2868 q^{33} - 9472 q^{37} + 1936 q^{45} - 26160 q^{51} + 51788 q^{55} + 4360 q^{57} - 93480 q^{61} + 85964 q^{63} - 43480 q^{67} - 75260 q^{73} + 163440 q^{75} + 11060 q^{81} + 55152 q^{85} - 130820 q^{87} + 14000 q^{91} + 17976 q^{93} + 64676 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(120, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
120.6.r.a 120.r 15.e $60$ $19.246$ None 120.6.r.a \(0\) \(0\) \(0\) \(-76\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{6}^{\mathrm{old}}(120, [\chi])\) into lower level spaces

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