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Properties

Label 116.4.a
Level $116$
Weight $4$
Character orbit 116.a
Rep. character $\chi_{116}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $3$
Sturm bound $60$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 116 = 2^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 116.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(60\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(116))\).

Total New Old
Modular forms 48 7 41
Cusp forms 42 7 35
Eisenstein series 6 0 6

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
\(-\)\(+\)$-$\(2\)
\(-\)\(-\)$+$\(5\)
Plus space\(+\)\(5\)
Minus space\(-\)\(2\)

Trace form

\( 7 q - 12 q^{7} + 105 q^{9} + O(q^{10}) \) \( 7 q - 12 q^{7} + 105 q^{9} + 8 q^{11} + 60 q^{13} + 152 q^{15} + 110 q^{17} - 4 q^{19} + 88 q^{21} + 92 q^{23} + 215 q^{25} + 36 q^{27} + 87 q^{29} + 288 q^{31} - 366 q^{33} - 476 q^{35} - 98 q^{37} - 1016 q^{39} + 410 q^{41} - 856 q^{43} + 498 q^{45} + 280 q^{47} + 487 q^{49} - 772 q^{51} - 688 q^{53} - 384 q^{55} - 624 q^{57} - 64 q^{59} + 234 q^{61} - 1696 q^{63} - 1346 q^{65} + 396 q^{67} + 164 q^{69} - 632 q^{71} + 1762 q^{73} - 348 q^{75} + 552 q^{77} + 1576 q^{79} + 1503 q^{81} - 1264 q^{83} + 504 q^{85} + 1738 q^{89} + 1244 q^{91} + 2134 q^{93} - 1296 q^{95} - 422 q^{97} - 132 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(116))\) 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
116.4.a.a 116.a 1.a $2$ $6.844$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(-10\) \(-20\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-5+2\beta )q^{5}+(-10+4\beta )q^{7}+\cdots\)
116.4.a.b 116.a 1.a $2$ $6.844$ \(\Q(\sqrt{22}) \) None \(0\) \(10\) \(30\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(5+\beta )q^{3}+15q^{5}-2\beta q^{7}+(20+10\beta )q^{9}+\cdots\)
116.4.a.c 116.a 1.a $3$ $6.844$ 3.3.148344.1 None \(0\) \(-10\) \(-20\) \(8\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-3-\beta _{1})q^{3}+(-7+\beta _{2})q^{5}+(4+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(116))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(116)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 2}\)