Properties

Label 116.2.a
Level $116$
Weight $2$
Character orbit 116.a
Rep. character $\chi_{116}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $3$
Sturm bound $30$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 116 = 2^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 116.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(30\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(116))\).

Total New Old
Modular forms 18 3 15
Cusp forms 13 3 10
Eisenstein series 5 0 5

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

\(2\)\(29\)FrickeDim
\(-\)\(+\)$-$\(3\)
Plus space\(+\)\(0\)
Minus space\(-\)\(3\)

Trace form

\( 3 q + 4 q^{5} + 4 q^{7} + 5 q^{9} + O(q^{10}) \) \( 3 q + 4 q^{5} + 4 q^{7} + 5 q^{9} - 4 q^{11} + 4 q^{13} - 10 q^{15} - 2 q^{17} - 6 q^{19} - 8 q^{21} - 8 q^{23} + 7 q^{25} - 18 q^{27} - 3 q^{29} + 8 q^{31} - 6 q^{33} - 8 q^{35} + 2 q^{37} + 18 q^{39} - 6 q^{41} + 4 q^{43} + 10 q^{45} - 12 q^{47} + 27 q^{49} - 8 q^{51} + 8 q^{53} + 18 q^{55} - 28 q^{57} - 4 q^{59} + 22 q^{61} + 36 q^{63} + 2 q^{65} + 4 q^{67} + 20 q^{69} + 12 q^{71} - 6 q^{73} - 10 q^{75} - 40 q^{77} + 4 q^{79} - q^{81} + 28 q^{83} - 16 q^{85} + 2 q^{89} - 24 q^{91} - 34 q^{93} + 12 q^{95} + 18 q^{97} - 18 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(116))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 29
116.2.a.a 116.a 1.a $1$ $0.926$ \(\Q\) None \(0\) \(-3\) \(3\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+3q^{5}+4q^{7}+6q^{9}-q^{11}+\cdots\)
116.2.a.b 116.a 1.a $1$ $0.926$ \(\Q\) None \(0\) \(1\) \(3\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}-4q^{7}-2q^{9}+3q^{11}+\cdots\)
116.2.a.c 116.a 1.a $1$ $0.926$ \(\Q\) None \(0\) \(2\) \(-2\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{5}+4q^{7}+q^{9}-6q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(116))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(116)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 2}\)