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Properties

Label 220.2.b
Level $220$
Weight $2$
Character orbit 220.b
Rep. character $\chi_{220}(89,\cdot)$
Character field $\Q$
Dimension $6$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
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 42 6 36
Cusp forms 30 6 24
Eisenstein series 12 0 12

Trace form

\( 6 q - q^{5} - 4 q^{9} + 2 q^{11} + 11 q^{15} - 8 q^{19} - 12 q^{21} + 3 q^{25} + 16 q^{29} + 6 q^{31} - 2 q^{35} - 32 q^{39} + 20 q^{45} - 14 q^{49} + 12 q^{51} + 3 q^{55} - 42 q^{59} - 8 q^{65} - 2 q^{69}+ \cdots - 16 q^{99}+O(q^{100}) \) 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.b.a 220.b 5.b $2$ $1.757$ \(\Q(\sqrt{-1}) \) None 220.2.b.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta-1)q^{5}+\beta q^{7}+3 q^{9}-q^{11}+\cdots\)
220.2.b.b 220.b 5.b $4$ $1.757$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None 220.2.b.b \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{2}-\beta _{3})q^{7}+\cdots\)

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

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