Properties

Label 440.2.p
Level $440$
Weight $2$
Character orbit 440.p
Rep. character $\chi_{440}(131,\cdot)$
Character field $\Q$
Dimension $48$
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.p (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 88 \)
Character field: \(\Q\)
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 76 48 28
Cusp forms 68 48 20
Eisenstein series 8 0 8

Trace form

\( 48 q + 4 q^{4} + 48 q^{9} + O(q^{10}) \) \( 48 q + 4 q^{4} + 48 q^{9} - 8 q^{11} + 16 q^{16} - 4 q^{20} - 4 q^{22} - 48 q^{25} - 20 q^{26} - 8 q^{33} - 8 q^{34} + 24 q^{36} - 44 q^{44} - 96 q^{48} + 48 q^{49} + 8 q^{58} + 16 q^{59} - 28 q^{60} + 4 q^{64} + 76 q^{66} - 80 q^{67} + 20 q^{70} + 8 q^{78} - 16 q^{80} + 64 q^{81} + 88 q^{82} - 28 q^{86} + 8 q^{88} - 112 q^{91} + 8 q^{92} - 8 q^{99} + O(q^{100}) \)

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.p.a 440.p 88.g $48$ $3.513$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(440, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 2}\)