Properties

Label 880.2.f
Level $880$
Weight $2$
Character orbit 880.f
Rep. character $\chi_{880}(351,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $5$
Sturm bound $288$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 44 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(288\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(19\)

Dimensions

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

Total New Old
Modular forms 156 24 132
Cusp forms 132 24 108
Eisenstein series 24 0 24

Trace form

\( 24 q + O(q^{10}) \) \( 24 q + 24 q^{25} + 24 q^{33} + 48 q^{49} - 48 q^{53} + 96 q^{69} + 24 q^{77} - 72 q^{81} - 24 q^{89} - 96 q^{93} - 48 q^{97} + O(q^{100}) \)

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.f.a 880.f 44.c $2$ $7.027$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}-q^{5}+q^{9}+(-3-\beta )q^{11}+\cdots\)
880.2.f.b 880.f 44.c $2$ $7.027$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}-q^{5}+q^{9}+(3-\beta )q^{11}-3\beta q^{13}+\cdots\)
880.2.f.c 880.f 44.c $4$ $7.027$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+q^{5}-2\beta _{2}q^{7}+q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
880.2.f.d 880.f 44.c $8$ $7.027$ 8.0.170772624.1 None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}-q^{5}+\beta _{1}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots\)
880.2.f.e 880.f 44.c $8$ $7.027$ 8.0.170772624.1 None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+q^{5}+\beta _{2}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 3}\)