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Properties

Label 113.2.a
Level $113$
Weight $2$
Character orbit 113.a
Rep. character $\chi_{113}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $4$
Sturm bound $19$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 113 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 113.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(19\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(113))\).

Total New Old
Modular forms 10 10 0
Cusp forms 9 9 0
Eisenstein series 1 1 0

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

\(113\)Dim
\(+\)\(3\)
\(-\)\(6\)

Trace form

\( 9 q - 3 q^{2} - 2 q^{3} + 5 q^{4} - 2 q^{5} + 4 q^{7} - 9 q^{8} + 7 q^{9} + O(q^{10}) \) \( 9 q - 3 q^{2} - 2 q^{3} + 5 q^{4} - 2 q^{5} + 4 q^{7} - 9 q^{8} + 7 q^{9} - 4 q^{10} + 2 q^{12} - 2 q^{13} + 2 q^{14} - 10 q^{15} + q^{16} - 2 q^{17} - q^{18} + 4 q^{20} + 18 q^{21} - 6 q^{22} - 6 q^{23} - 6 q^{24} + 5 q^{25} + 4 q^{26} - 8 q^{27} - 6 q^{28} - 6 q^{30} - 6 q^{31} - q^{32} - 2 q^{33} - 34 q^{34} - 12 q^{35} - 17 q^{36} + 8 q^{38} + 22 q^{39} - 4 q^{40} - 12 q^{41} + 12 q^{42} + 22 q^{43} + 4 q^{44} - 14 q^{45} + 14 q^{46} + 14 q^{47} + 22 q^{48} + 37 q^{49} + 11 q^{50} + 6 q^{51} + 18 q^{52} - 28 q^{53} + 4 q^{54} - 2 q^{55} - 10 q^{56} - 22 q^{57} + 30 q^{58} + 18 q^{59} - 12 q^{60} - 24 q^{61} + 2 q^{62} + 8 q^{63} + 7 q^{64} - 30 q^{65} - 38 q^{66} - 6 q^{67} + 68 q^{68} - 18 q^{69} + 40 q^{70} + 20 q^{71} - 25 q^{72} - 6 q^{73} - 4 q^{74} + 28 q^{75} - 10 q^{76} - 14 q^{77} - 42 q^{78} + 16 q^{79} - 14 q^{80} + 9 q^{81} + 34 q^{82} + 12 q^{83} + 8 q^{84} - 12 q^{85} - 18 q^{86} + 6 q^{87} + 10 q^{88} - 24 q^{89} - 18 q^{90} + 22 q^{91} - 22 q^{92} + 20 q^{93} + 28 q^{94} + 16 q^{95} - 48 q^{96} - 6 q^{97} - 39 q^{98} - 58 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(113))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 113
113.2.a.a 113.a 1.a $1$ $0.902$ \(\Q\) None \(-1\) \(2\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}-q^{4}+2q^{5}-2q^{6}+3q^{8}+\cdots\)
113.2.a.b 113.a 1.a $2$ $0.902$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(0\) \(8\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}-q^{4}-2\beta q^{5}+(1+\cdots)q^{6}+\cdots\)
113.2.a.c 113.a 1.a $3$ $0.902$ \(\Q(\zeta_{14})^+\) None \(-2\) \(-5\) \(-1\) \(-10\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+\cdots\)
113.2.a.d 113.a 1.a $3$ $0.902$ 3.3.321.1 None \(-2\) \(-1\) \(-3\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}-\beta _{1}q^{3}+(3-\beta _{1})q^{4}+\cdots\)