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Properties

Label 220.2.k
Level $220$
Weight $2$
Character orbit 220.k
Rep. character $\chi_{220}(153,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
Newform subspaces $2$
Sturm bound $72$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 220.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(220, [\chi])\).

Total New Old
Modular forms 84 12 72
Cusp forms 60 12 48
Eisenstein series 24 0 24

Trace form

\( 12 q - 2 q^{3} - 4 q^{5} - 4 q^{15} - 6 q^{23} - 14 q^{25} + 10 q^{27} - 16 q^{31} + 22 q^{33} + 34 q^{37} + 26 q^{45} - 28 q^{47} - 36 q^{53} - 22 q^{55} - 38 q^{67} - 4 q^{71} + 60 q^{75} - 44 q^{77}+ \cdots + 54 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(220, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
220.2.k.a 220.k 55.e $4$ $1.757$ \(\Q(i, \sqrt{11})\) None 220.2.k.a \(0\) \(-4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{1})q^{3}+(-1+2\beta _{1})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
220.2.k.b 220.k 55.e $8$ $1.757$ 8.0.303595776.1 \(\Q(\sqrt{-11}) \) 220.2.k.b \(0\) \(2\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q-\beta _{1}q^{3}+(\beta _{2}+\beta _{6})q^{5}+(\beta _{1}-3\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(220, [\chi])\) into lower level spaces

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