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Properties

Label 880.2.v
Level $880$
Weight $2$
Character orbit 880.v
Rep. character $\chi_{880}(131,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $192$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 176 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(880, [\chi])\).

Total New Old
Modular forms 296 192 104
Cusp forms 280 192 88
Eisenstein series 16 0 16

Trace form

\( 192 q - 8 q^{4} + O(q^{10}) \) \( 192 q - 8 q^{4} + 8 q^{11} + 16 q^{14} + 40 q^{16} - 8 q^{20} + 20 q^{22} + 32 q^{23} + 32 q^{26} + 40 q^{34} + 32 q^{37} + 40 q^{42} - 48 q^{44} + 40 q^{48} - 192 q^{49} - 32 q^{53} - 48 q^{56} + 40 q^{58} + 16 q^{59} + 56 q^{60} - 56 q^{64} + 40 q^{66} - 80 q^{67} + 8 q^{70} + 32 q^{71} + 16 q^{77} - 152 q^{78} - 32 q^{80} - 192 q^{81} - 80 q^{82} - 160 q^{86} + 80 q^{88} - 80 q^{91} - 72 q^{92} + 72 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(880, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
880.2.v.a 880.v 176.i $192$ $7.027$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(880, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)