Properties

Label 110.2.j
Level $110$
Weight $2$
Character orbit 110.j
Rep. character $\chi_{110}(9,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $24$
Newform subspaces $2$
Sturm bound $36$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 110 = 2 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 110.j (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 88 24 64
Cusp forms 56 24 32
Eisenstein series 32 0 32

Trace form

\( 24q + 6q^{4} - 2q^{5} + 4q^{6} - 10q^{9} + O(q^{10}) \) \( 24q + 6q^{4} - 2q^{5} + 4q^{6} - 10q^{9} - 4q^{10} - 2q^{11} - 6q^{14} + 14q^{15} - 6q^{16} - 16q^{19} + 2q^{20} - 40q^{21} - 4q^{24} - 6q^{25} - 4q^{26} - 4q^{29} - 26q^{30} - 8q^{31} + 8q^{34} - 52q^{35} - 10q^{36} - 36q^{39} - 6q^{40} + 46q^{41} + 22q^{44} + 44q^{45} + 32q^{46} + 68q^{49} - 4q^{50} + 12q^{51} + 64q^{54} + 36q^{55} - 4q^{56} + 16q^{60} + 56q^{61} + 6q^{64} + 44q^{65} - 68q^{66} + 32q^{69} + 24q^{70} - 60q^{71} + 64q^{75} - 4q^{76} - 4q^{79} + 8q^{80} - 138q^{81} - 20q^{84} - 38q^{85} - 8q^{86} - 108q^{89} + 10q^{90} - 14q^{91} - 30q^{94} - 50q^{95} + 4q^{96} + 6q^{99} + O(q^{100}) \)

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.j.a \(8\) \(0.878\) \(\Q(\zeta_{20})\) None \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{20}q^{2}+(-2\zeta_{20}-2\zeta_{20}^{5})q^{3}+\cdots\)
110.2.j.b \(16\) \(0.878\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-6\) \(0\) \(q-\beta _{6}q^{2}+(-\beta _{6}-\beta _{10}-\beta _{12})q^{3}+\cdots\)

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

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