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 $5$

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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

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

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.b.a 110.b 5.b $2$ $0.878$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}+(-2+i)q^{5}+\cdots\)
110.2.b.b 110.b 5.b $2$ $0.878$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-2iq^{3}-q^{4}+(1-2i)q^{5}+\cdots\)
110.2.b.c 110.b 5.b $2$ $0.878$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+3iq^{3}-q^{4}+(2-i)q^{5}-3q^{6}+\cdots\)

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

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