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Properties

Label 220.3.j
Level $220$
Weight $3$
Character orbit 220.j
Rep. character $\chi_{220}(133,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $20$
Newform subspaces $1$
Sturm bound $108$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 220.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(108\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(220, [\chi])\).

Total New Old
Modular forms 156 20 136
Cusp forms 132 20 112
Eisenstein series 24 0 24

Trace form

\( 20 q - 2 q^{3} + 8 q^{5} - 28 q^{13} + 28 q^{15} + 24 q^{17} + 106 q^{23} - 6 q^{25} - 50 q^{27} + 88 q^{31} - 22 q^{33} - 252 q^{35} + 2 q^{37} + 72 q^{41} + 168 q^{43} + 38 q^{45} + 108 q^{47} + 112 q^{51}+ \cdots - 542 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(220, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
220.3.j.a 220.j 5.c $20$ $5.995$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 220.3.j.a \(0\) \(-2\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{3}-\beta _{13}q^{5}+(-\beta _{3}-\beta _{11})q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(220, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(220, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)