Properties

Label 110.2.f
Level $110$
Weight $2$
Character orbit 110.f
Rep. character $\chi_{110}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
Newform subspaces $3$
Sturm bound $36$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 110 = 2 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 110.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(36\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(3\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(110, [\chi])\).

Total New Old
Modular forms 44 12 32
Cusp forms 28 12 16
Eisenstein series 16 0 16

Trace form

\( 12 q + 4 q^{3} + 8 q^{5} + O(q^{10}) \) \( 12 q + 4 q^{3} + 8 q^{5} - 12 q^{11} - 4 q^{12} - 4 q^{15} - 12 q^{16} + 4 q^{20} + 4 q^{22} - 12 q^{23} - 20 q^{25} - 8 q^{26} - 8 q^{27} - 16 q^{31} + 4 q^{33} + 4 q^{36} - 20 q^{37} - 24 q^{38} + 40 q^{42} + 44 q^{45} + 20 q^{47} - 4 q^{48} + 60 q^{53} - 16 q^{55} + 8 q^{56} + 32 q^{58} + 20 q^{60} + 16 q^{66} - 20 q^{67} + 16 q^{70} + 56 q^{71} - 84 q^{75} + 16 q^{77} - 16 q^{78} - 8 q^{80} + 28 q^{81} - 64 q^{86} + 4 q^{88} - 32 q^{91} + 12 q^{92} - 56 q^{93} - 12 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(110, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
110.2.f.a 110.f 55.e $4$ $0.878$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
110.2.f.b 110.f 55.e $4$ $0.878$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+(1-\zeta_{8}+\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
110.2.f.c 110.f 55.e $4$ $0.878$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+(1+\zeta_{8}+\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(110, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(110, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)