Properties

Label 880.2.b
Level $880$
Weight $2$
Character orbit 880.b
Rep. character $\chi_{880}(529,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $10$
Sturm bound $288$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(288\)
Trace bound: \(15\)
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 156 30 126
Cusp forms 132 30 102
Eisenstein series 24 0 24

Trace form

\( 30 q + 2 q^{5} - 30 q^{9} + O(q^{10}) \) \( 30 q + 2 q^{5} - 30 q^{9} - 6 q^{11} + 6 q^{15} + 8 q^{19} - 8 q^{21} + 2 q^{25} + 4 q^{29} + 4 q^{31} - 12 q^{35} - 4 q^{41} - 10 q^{45} - 30 q^{49} - 8 q^{51} + 44 q^{59} + 36 q^{61} - 24 q^{65} - 8 q^{69} + 20 q^{71} - 58 q^{75} - 40 q^{79} + 70 q^{81} - 8 q^{85} + 12 q^{89} + 16 q^{91} - 24 q^{95} + 18 q^{99} + O(q^{100}) \)

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.b.a 880.b 5.b $2$ $7.027$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-2-i)q^{5}+3iq^{7}+2q^{9}+\cdots\)
880.2.b.b 880.b 5.b $2$ $7.027$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-1-i)q^{5}+iq^{7}-q^{9}+\cdots\)
880.2.b.c 880.b 5.b $2$ $7.027$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{5}-iq^{7}+3q^{9}+q^{11}+\cdots\)
880.2.b.d 880.b 5.b $2$ $7.027$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(1+i)q^{5}-2iq^{7}-q^{9}-q^{11}+\cdots\)
880.2.b.e 880.b 5.b $2$ $7.027$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(1-i)q^{5}-q^{9}-q^{11}+iq^{13}+\cdots\)
880.2.b.f 880.b 5.b $2$ $7.027$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+(2+i)q^{5}-iq^{7}-6q^{9}+\cdots\)
880.2.b.g 880.b 5.b $2$ $7.027$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(2-i)q^{5}+iq^{7}+2q^{9}+q^{11}+\cdots\)
880.2.b.h 880.b 5.b $4$ $7.027$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(-1+\beta _{3})q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
880.2.b.i 880.b 5.b $4$ $7.027$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{2})q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2}-\beta _{3})q^{7}+\cdots\)
880.2.b.j 880.b 5.b $8$ $7.027$ 8.0.\(\cdots\).2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{4}q^{5}+(\beta _{1}-\beta _{3}-\beta _{4})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)