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Properties

Label 220.6.b
Level $220$
Weight $6$
Character orbit 220.b
Rep. character $\chi_{220}(89,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $2$
Sturm bound $216$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
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: \(216\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(220, [\chi])\).

Total New Old
Modular forms 186 26 160
Cusp forms 174 26 148
Eisenstein series 12 0 12

Trace form

\( 26 q - 31 q^{5} - 2748 q^{9} + O(q^{10}) \) \( 26 q - 31 q^{5} - 2748 q^{9} + 242 q^{11} + 1631 q^{15} - 2440 q^{19} + 2908 q^{21} + 1913 q^{25} - 19904 q^{29} - 4306 q^{31} + 23438 q^{35} + 2784 q^{39} - 1648 q^{41} + 33380 q^{45} - 60234 q^{49} - 72756 q^{51} - 6897 q^{55} + 88614 q^{59} + 39360 q^{61} - 131368 q^{65} + 32738 q^{69} - 116042 q^{71} - 154303 q^{75} + 104284 q^{79} + 129582 q^{81} - 88818 q^{85} - 51434 q^{89} + 104000 q^{91} + 25908 q^{95} + 56144 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(220, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
220.6.b.a 220.b 5.b $12$ $35.284$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 220.6.b.a \(0\) \(0\) \(13\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(1+\beta _{4})q^{5}+\beta _{8}q^{7}+(-134+\cdots)q^{9}+\cdots\)
220.6.b.b 220.b 5.b $14$ $35.284$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None 220.6.b.b \(0\) \(0\) \(-44\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-3+\beta _{4})q^{5}+(-\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(220, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(220, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)