Properties

Label 110.2.a
Level $110$
Weight $2$
Character orbit 110.a
Rep. character $\chi_{110}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $4$
Sturm bound $36$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 110 = 2 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 110.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(36\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(110))\).

Total New Old
Modular forms 22 5 17
Cusp forms 15 5 10
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(5\)\(11\)FrickeDim
\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(5\)

Trace form

\( 5 q - q^{2} + 5 q^{4} + q^{5} + 8 q^{7} - q^{8} + 5 q^{9} + O(q^{10}) \) \( 5 q - q^{2} + 5 q^{4} + q^{5} + 8 q^{7} - q^{8} + 5 q^{9} - q^{10} - q^{11} + 2 q^{13} - 4 q^{14} - 4 q^{15} + 5 q^{16} - 10 q^{17} - 13 q^{18} + 4 q^{19} + q^{20} - 16 q^{21} + q^{22} - 12 q^{23} + 5 q^{25} - 10 q^{26} - 24 q^{27} + 8 q^{28} - 10 q^{29} - 4 q^{31} - q^{32} - 10 q^{34} + 5 q^{36} + 14 q^{37} + 4 q^{38} + 8 q^{39} - q^{40} + 2 q^{41} + 8 q^{42} + 12 q^{43} - q^{44} + 13 q^{45} + 12 q^{46} + 4 q^{47} + 17 q^{49} - q^{50} - 8 q^{51} + 2 q^{52} + 14 q^{53} + 24 q^{54} - q^{55} - 4 q^{56} + 2 q^{58} - 4 q^{59} - 4 q^{60} + 6 q^{61} + 8 q^{62} + 8 q^{63} + 5 q^{64} - 6 q^{65} - 4 q^{66} + 40 q^{67} - 10 q^{68} - 24 q^{69} + 8 q^{70} + 4 q^{71} - 13 q^{72} - 2 q^{73} + 2 q^{74} + 4 q^{76} + 8 q^{77} + 8 q^{78} + q^{80} + 29 q^{81} - 10 q^{82} - 12 q^{83} - 16 q^{84} - 10 q^{85} + 12 q^{86} - 32 q^{87} + q^{88} - 18 q^{89} - 13 q^{90} - 8 q^{91} - 12 q^{92} - 16 q^{93} + 4 q^{94} + 20 q^{95} - 22 q^{97} - 25 q^{98} - 13 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(110))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 11
110.2.a.a 110.a 1.a $1$ $0.878$ \(\Q\) None 110.2.a.a \(-1\) \(1\) \(-1\) \(5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+5q^{7}+\cdots\)
110.2.a.b 110.a 1.a $1$ $0.878$ \(\Q\) None 110.2.a.b \(1\) \(-1\) \(1\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots\)
110.2.a.c 110.a 1.a $1$ $0.878$ \(\Q\) None 110.2.a.c \(1\) \(1\) \(-1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
110.2.a.d 110.a 1.a $2$ $0.878$ \(\Q(\sqrt{33}) \) None 110.2.a.d \(-2\) \(-1\) \(2\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+\beta q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(110))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(110)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 2}\)