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Properties

Label 880.2.bi
Level $880$
Weight $2$
Character orbit 880.bi
Rep. character $\chi_{880}(219,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $280$
Newform subspaces $4$
Sturm bound $288$
Trace bound $2$

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Defining parameters

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

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

\( 280 q - 8 q^{4} - 4 q^{5} + O(q^{10}) \) \( 280 q - 8 q^{4} - 4 q^{5} - 4 q^{11} - 16 q^{14} - 8 q^{16} - 4 q^{20} - 80 q^{26} - 24 q^{34} + 24 q^{36} + 24 q^{44} + 4 q^{45} + 216 q^{49} + 28 q^{55} - 16 q^{56} + 8 q^{59} + 36 q^{60} - 104 q^{64} + 8 q^{66} + 16 q^{69} - 8 q^{70} - 48 q^{71} - 48 q^{75} - 88 q^{80} - 232 q^{81} - 16 q^{86} - 80 q^{91} + 76 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
880.2.bi.a 880.bi 880.ai $4$ $7.027$ \(\Q(i, \sqrt{6})\) None 880.2.bi.a \(-4\) \(0\) \(-4\) \(-12\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}+2\beta _{2}q^{4}+\cdots\)
880.2.bi.b 880.bi 880.ai $4$ $7.027$ \(\Q(i, \sqrt{6})\) None 880.2.bi.a \(4\) \(0\) \(-4\) \(12\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{2})q^{2}+\beta _{1}q^{3}+2\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
880.2.bi.c 880.bi 880.ai $16$ $7.027$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) \(\Q(\sqrt{-55}) \) 880.2.bi.c \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q-\beta _{13}q^{2}+\beta _{9}q^{4}+(\beta _{1}-\beta _{3})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
880.2.bi.d 880.bi 880.ai $256$ $7.027$ None 880.2.bi.d \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$