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Properties

Label 220.2.l
Level $220$
Weight $2$
Character orbit 220.l
Rep. character $\chi_{220}(23,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $60$
Newform subspaces $4$
Sturm bound $72$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 220.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(72\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 80 60 20
Cusp forms 64 60 4
Eisenstein series 16 0 16

Trace form

\( 60 q - 8 q^{6} - 12 q^{8} + O(q^{10}) \) \( 60 q - 8 q^{6} - 12 q^{8} - 4 q^{13} - 20 q^{17} + 28 q^{18} - 16 q^{21} - 20 q^{25} + 8 q^{26} - 20 q^{28} - 40 q^{30} - 40 q^{32} + 32 q^{36} + 20 q^{37} - 40 q^{38} + 40 q^{40} + 20 q^{45} + 40 q^{46} + 8 q^{48} + 4 q^{50} + 4 q^{52} - 20 q^{53} - 8 q^{56} - 32 q^{57} - 8 q^{58} - 80 q^{60} - 64 q^{61} - 36 q^{62} - 12 q^{65} + 52 q^{68} + 16 q^{70} - 20 q^{72} + 52 q^{73} + 8 q^{76} - 16 q^{80} + 20 q^{81} - 80 q^{82} - 20 q^{85} - 48 q^{86} + 24 q^{88} + 60 q^{90} + 56 q^{92} + 24 q^{93} + 16 q^{96} + 20 q^{97} - 64 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.l.a 220.l 20.e $2$ $1.757$ \(\Q(\sqrt{-1}) \) None 220.2.l.a \(-2\) \(-4\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{2}+(-2-2i)q^{3}-2iq^{4}+\cdots\)
220.2.l.b 220.l 20.e $2$ $1.757$ \(\Q(\sqrt{-1}) \) None 220.2.l.a \(2\) \(4\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{2}+(2+2i)q^{3}-2iq^{4}+(-1+\cdots)q^{5}+\cdots\)
220.2.l.c 220.l 20.e $28$ $1.757$ None 220.2.l.c \(-2\) \(-4\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{4}]$
220.2.l.d 220.l 20.e $28$ $1.757$ None 220.2.l.c \(2\) \(4\) \(2\) \(2\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(220, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)