Properties

Label 110.2.b
Level $110$
Weight $2$
Character orbit 110.b
Rep. character $\chi_{110}(89,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $3$
Sturm bound $36$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

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

Dimensions

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

Total New Old
Modular forms 22 6 16
Cusp forms 14 6 8
Eisenstein series 8 0 8

Trace form

\( 6q - 6q^{4} + 2q^{5} - 4q^{6} - 10q^{9} + O(q^{10}) \) \( 6q - 6q^{4} + 2q^{5} - 4q^{6} - 10q^{9} + 4q^{10} + 2q^{11} - 4q^{14} - 4q^{15} + 6q^{16} + 16q^{19} - 2q^{20} + 4q^{24} + 6q^{25} + 4q^{26} + 4q^{29} - 4q^{30} - 12q^{31} - 8q^{34} - 8q^{35} + 10q^{36} + 16q^{39} - 4q^{40} - 36q^{41} - 2q^{44} - 34q^{45} - 12q^{46} + 22q^{49} + 24q^{50} + 48q^{51} + 16q^{54} - 6q^{55} + 4q^{56} + 4q^{60} - 36q^{61} - 6q^{64} + 16q^{65} + 8q^{66} - 32q^{69} + 16q^{70} - 20q^{71} + 16q^{75} - 16q^{76} - 16q^{79} + 2q^{80} - 2q^{81} + 8q^{85} + 8q^{86} + 8q^{89} - 20q^{90} + 24q^{91} - 20q^{94} - 4q^{96} + 14q^{99} + O(q^{100}) \)

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.b.a \(2\) \(0.878\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}+(-2+i)q^{5}+\cdots\)
110.2.b.b \(2\) \(0.878\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{2}-2iq^{3}-q^{4}+(1-2i)q^{5}+\cdots\)
110.2.b.c \(2\) \(0.878\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{2}+3iq^{3}-q^{4}+(2-i)q^{5}-3q^{6}+\cdots\)

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

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