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Properties

Label 880.2.t
Level $880$
Weight $2$
Character orbit 880.t
Rep. character $\chi_{880}(197,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $280$
Newform subspaces $2$
Sturm bound $288$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 880 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

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

Trace form

\( 280 q - 4 q^{5} - 264 q^{9} + O(q^{10}) \) \( 280 q - 4 q^{5} - 264 q^{9} - 4 q^{11} - 8 q^{12} - 8 q^{15} - 8 q^{16} - 4 q^{20} - 4 q^{22} + 24 q^{26} - 16 q^{31} - 4 q^{33} + 8 q^{34} - 40 q^{36} - 24 q^{38} - 24 q^{42} - 40 q^{44} - 12 q^{45} - 8 q^{47} + 8 q^{48} - 8 q^{53} - 56 q^{56} + 56 q^{58} - 16 q^{59} + 44 q^{60} + 4 q^{66} - 8 q^{67} + 24 q^{69} + 48 q^{70} - 24 q^{75} - 32 q^{77} - 32 q^{78} + 104 q^{80} + 200 q^{81} - 8 q^{82} - 40 q^{88} - 24 q^{91} + 96 q^{92} - 8 q^{97} - 20 q^{99} + O(q^{100}) \)

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.t.a 880.t 880.t $8$ $7.027$ 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta _{1}+\beta _{6})q^{2}+\beta _{3}q^{3}+2q^{4}+\beta _{4}q^{5}+\cdots\)
880.2.t.b 880.t 880.t $272$ $7.027$ None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$