Properties

Label 110.2.k
Level $110$
Weight $2$
Character orbit 110.k
Rep. character $\chi_{110}(7,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $48$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 110 = 2 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 110.k (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 176 48 128
Cusp forms 112 48 64
Eisenstein series 64 0 64

Trace form

\( 48q - 4q^{3} - 8q^{5} - 20q^{7} + O(q^{10}) \) \( 48q - 4q^{3} - 8q^{5} - 20q^{7} + 12q^{11} - 16q^{12} - 16q^{15} + 12q^{16} - 20q^{17} - 4q^{20} - 4q^{22} - 8q^{23} - 20q^{25} + 8q^{26} + 8q^{27} - 20q^{28} + 16q^{31} - 104q^{33} - 4q^{36} + 20q^{37} - 36q^{38} - 20q^{41} - 20q^{42} + 16q^{45} + 40q^{46} + 40q^{47} + 4q^{48} + 40q^{50} + 40q^{51} + 40q^{52} + 96q^{55} - 8q^{56} + 48q^{58} + 20q^{60} + 80q^{61} + 40q^{62} + 100q^{63} + 24q^{66} + 20q^{68} - 56q^{70} - 56q^{71} - 20q^{73} - 76q^{75} - 96q^{77} + 16q^{78} - 12q^{80} - 68q^{81} - 80q^{85} - 56q^{86} - 4q^{88} - 80q^{90} - 68q^{91} - 12q^{92} + 76q^{93} + 20q^{95} + 72q^{97} + O(q^{100}) \)

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.k.a \(48\) \(0.878\) None \(0\) \(-4\) \(-8\) \(-20\)

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

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