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Properties

Label 880.2.bz
Level $880$
Weight $2$
Character orbit 880.bz
Rep. character $\chi_{880}(271,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $96$
Newform subspaces $4$
Sturm bound $288$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.bz (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 44 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 4 \)
Sturm bound: \(288\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 624 96 528
Cusp forms 528 96 432
Eisenstein series 96 0 96

Trace form

\( 96 q + O(q^{10}) \) \( 96 q - 24 q^{25} + 36 q^{33} + 60 q^{41} + 12 q^{49} + 48 q^{53} + 60 q^{57} - 96 q^{69} - 144 q^{77} - 108 q^{81} - 96 q^{89} + 96 q^{93} - 132 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
880.2.bz.a 880.bz 44.g $16$ $7.027$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 880.2.bz.a \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-\beta _{7}+\beta _{10}-\beta _{11}+\beta _{12}-\beta _{13}+\cdots)q^{3}+\cdots\)
880.2.bz.b 880.bz 44.g $16$ $7.027$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 880.2.bz.b \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\beta _{1}+\beta _{5}+\beta _{9}+\beta _{10}-\beta _{14})q^{3}+\cdots\)
880.2.bz.c 880.bz 44.g $32$ $7.027$ None 880.2.bz.c \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{10}]$
880.2.bz.d 880.bz 44.g $32$ $7.027$ None 880.2.bz.d \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{10}]$

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

\( S_{2}^{\mathrm{old}}(880, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)