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Properties

Label 880.2.bo
Level $880$
Weight $2$
Character orbit 880.bo
Rep. character $\chi_{880}(81,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $96$
Newform subspaces $11$
Sturm bound $288$
Trace bound $7$

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Defining parameters

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

\( 96 q + 4 q^{7} - 16 q^{9} + O(q^{10}) \) \( 96 q + 4 q^{7} - 16 q^{9} + 4 q^{11} + 8 q^{17} + 8 q^{23} - 24 q^{25} - 16 q^{29} - 20 q^{33} - 12 q^{35} + 24 q^{37} + 36 q^{39} - 20 q^{41} + 56 q^{43} + 36 q^{47} - 36 q^{49} + 36 q^{51} + 40 q^{53} - 20 q^{57} - 16 q^{59} + 16 q^{61} + 20 q^{63} + 8 q^{65} + 40 q^{67} + 32 q^{69} - 28 q^{71} + 24 q^{73} - 24 q^{77} - 84 q^{79} - 68 q^{81} - 36 q^{83} - 168 q^{87} - 16 q^{89} - 64 q^{91} + 32 q^{93} + 16 q^{95} - 28 q^{97} - 112 q^{99} + O(q^{100}) \)

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.bo.a 880.bo 11.c $4$ $7.027$ \(\Q(\zeta_{10})\) None \(0\) \(-4\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-2\zeta_{10}-2\zeta_{10}^{3})q^{3}+\zeta_{10}q^{5}+\cdots\)
880.2.bo.b 880.bo 11.c $4$ $7.027$ \(\Q(\zeta_{10})\) None \(0\) \(-4\) \(1\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+\zeta_{10}q^{5}+\cdots\)
880.2.bo.c 880.bo 11.c $8$ $7.027$ 8.0.159390625.1 None \(0\) \(-5\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5}-\beta _{6}+\beta _{7})q^{3}+\cdots\)
880.2.bo.d 880.bo 11.c $8$ $7.027$ 8.0.13140625.1 None \(0\) \(-1\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}+\beta _{5})q^{3}+\beta _{7}q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
880.2.bo.e 880.bo 11.c $8$ $7.027$ 8.0.159390625.1 None \(0\) \(-1\) \(-2\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{1}q^{3}-\beta _{6}q^{5}+(2-3\beta _{2}-3\beta _{3}+\cdots)q^{7}+\cdots\)
880.2.bo.f 880.bo 11.c $8$ $7.027$ 8.0.26265625.1 None \(0\) \(1\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{1}+\beta _{7})q^{3}+\beta _{2}q^{5}+(1-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
880.2.bo.g 880.bo 11.c $8$ $7.027$ 8.0.682515625.5 None \(0\) \(4\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}-\beta _{3}+\beta _{5}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
880.2.bo.h 880.bo 11.c $8$ $7.027$ 8.0.13140625.1 None \(0\) \(5\) \(2\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\beta _{1}-\beta _{3}+\beta _{4}+\beta _{5}+\beta _{6})q^{3}+\cdots\)
880.2.bo.i 880.bo 11.c $12$ $7.027$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(1\) \(3\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{3}-\beta _{8})q^{3}-\beta _{6}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
880.2.bo.j 880.bo 11.c $12$ $7.027$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(1\) \(3\) \(8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}-\beta _{5})q^{3}+\beta _{8}q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
880.2.bo.k 880.bo 11.c $16$ $7.027$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(3\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{1}q^{3}+(-1+\beta _{4}-\beta _{10}+\beta _{12}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)