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Properties

Label 440.2.bo
Level $440$
Weight $2$
Character orbit 440.bo
Rep. character $\chi_{440}(17,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $144$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 440.bo (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(440, [\chi])\).

Total New Old
Modular forms 640 144 496
Cusp forms 512 144 368
Eisenstein series 128 0 128

Trace form

\( 144 q + O(q^{10}) \) \( 144 q - 4 q^{11} + 24 q^{23} + 24 q^{25} - 12 q^{27} - 16 q^{31} + 16 q^{37} - 60 q^{41} + 32 q^{45} - 28 q^{47} - 120 q^{51} + 12 q^{53} + 12 q^{55} + 80 q^{57} + 112 q^{67} - 48 q^{71} - 60 q^{73} + 28 q^{75} + 40 q^{77} + 4 q^{81} + 28 q^{91} - 96 q^{93} - 40 q^{95} - 60 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(440, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
440.2.bo.a 440.bo 55.l $144$ $3.513$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(440, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(440, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 2}\)