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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
110.2.f.a \(4\) \(0.878\) \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(8\) \(0\) \(q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
110.2.f.b \(4\) \(0.878\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+(1-\zeta_{8}+\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
110.2.f.c \(4\) \(0.878\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+(1+\zeta_{8}+\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)

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

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