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Properties

Label 880.2.cm
Level $880$
Weight $2$
Character orbit 880.cm
Rep. character $\chi_{880}(17,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $272$
Newform subspaces $4$
Sturm bound $288$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.cm (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 4 \)
Sturm bound: \(288\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 1248 304 944
Cusp forms 1056 272 784
Eisenstein series 192 32 160

Trace form

\( 272 q + 6 q^{3} - 6 q^{5} + 10 q^{7} + O(q^{10}) \) \( 272 q + 6 q^{3} - 6 q^{5} + 10 q^{7} + 16 q^{11} - 10 q^{13} + 18 q^{15} - 10 q^{17} - 8 q^{23} - 6 q^{25} + 30 q^{27} + 12 q^{31} - 10 q^{33} + 10 q^{35} - 6 q^{37} - 60 q^{41} - 36 q^{45} + 18 q^{47} + 140 q^{51} - 6 q^{53} - 26 q^{55} - 10 q^{57} - 20 q^{61} - 20 q^{63} - 32 q^{67} + 76 q^{71} - 50 q^{73} - 6 q^{75} - 22 q^{77} + 24 q^{81} - 90 q^{83} - 10 q^{85} + 28 q^{91} - 42 q^{93} + 10 q^{95} + 10 q^{97} + O(q^{100}) \)

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.cm.a 880.cm 55.l $32$ $7.027$ None 55.2.l.a \(0\) \(4\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{20}]$
880.2.cm.b 880.cm 55.l $48$ $7.027$ None 220.2.u.a \(0\) \(-2\) \(4\) \(-10\) $\mathrm{SU}(2)[C_{20}]$
880.2.cm.c 880.cm 55.l $48$ $7.027$ None 110.2.k.a \(0\) \(4\) \(-8\) \(20\) $\mathrm{SU}(2)[C_{20}]$
880.2.cm.d 880.cm 55.l $144$ $7.027$ None 440.2.bo.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$

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

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