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Properties

Label 114.4.a
Level $114$
Weight $4$
Character orbit 114.a
Rep. character $\chi_{114}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $6$
Sturm bound $80$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 114.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(80\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(114))\).

Total New Old
Modular forms 64 8 56
Cusp forms 56 8 48
Eisenstein series 8 0 8

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

\(2\)\(3\)\(19\)FrickeDim
\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(-\)\(+\)$-$\(1\)
\(+\)\(-\)\(-\)$+$\(1\)
\(-\)\(+\)\(+\)$-$\(1\)
\(-\)\(+\)\(-\)$+$\(2\)
\(-\)\(-\)\(+\)$+$\(2\)
Plus space\(+\)\(6\)
Minus space\(-\)\(2\)

Trace form

\( 8 q + 4 q^{2} + 32 q^{4} + 4 q^{5} - 12 q^{6} - 4 q^{7} + 16 q^{8} + 72 q^{9} + O(q^{10}) \) \( 8 q + 4 q^{2} + 32 q^{4} + 4 q^{5} - 12 q^{6} - 4 q^{7} + 16 q^{8} + 72 q^{9} + 64 q^{10} - 24 q^{11} + 20 q^{13} + 84 q^{15} + 128 q^{16} + 260 q^{17} + 36 q^{18} - 38 q^{19} + 16 q^{20} + 168 q^{22} + 180 q^{23} - 48 q^{24} + 340 q^{25} - 72 q^{26} - 16 q^{28} - 436 q^{29} - 120 q^{30} - 132 q^{31} + 64 q^{32} - 180 q^{33} + 8 q^{34} - 516 q^{35} + 288 q^{36} - 620 q^{37} - 24 q^{39} + 256 q^{40} + 412 q^{41} + 240 q^{42} - 876 q^{43} - 96 q^{44} + 36 q^{45} - 96 q^{46} - 624 q^{47} - 788 q^{49} - 36 q^{50} - 552 q^{51} + 80 q^{52} + 68 q^{53} - 108 q^{54} + 1196 q^{55} - 114 q^{57} - 688 q^{58} - 496 q^{59} + 336 q^{60} + 268 q^{61} - 1760 q^{62} - 36 q^{63} + 512 q^{64} + 32 q^{65} - 24 q^{66} - 32 q^{67} + 1040 q^{68} - 288 q^{69} - 960 q^{70} - 64 q^{71} + 144 q^{72} - 1948 q^{73} + 488 q^{74} - 1680 q^{75} - 152 q^{76} + 932 q^{77} + 528 q^{78} + 1140 q^{79} + 64 q^{80} + 648 q^{81} - 1280 q^{82} + 1084 q^{83} + 732 q^{85} - 2096 q^{86} + 132 q^{87} + 672 q^{88} + 1916 q^{89} + 576 q^{90} + 2744 q^{91} + 720 q^{92} - 360 q^{93} + 48 q^{94} + 1064 q^{95} - 192 q^{96} - 208 q^{97} + 1252 q^{98} - 216 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(114))\) 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 3 19
114.4.a.a 114.a 1.a $1$ $6.726$ \(\Q\) None \(-2\) \(-3\) \(-19\) \(9\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}-19q^{5}+6q^{6}+\cdots\)
114.4.a.b 114.a 1.a $1$ $6.726$ \(\Q\) None \(-2\) \(3\) \(-7\) \(-15\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-7q^{5}-6q^{6}+\cdots\)
114.4.a.c 114.a 1.a $1$ $6.726$ \(\Q\) None \(-2\) \(3\) \(12\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+12q^{5}-6q^{6}+\cdots\)
114.4.a.d 114.a 1.a $1$ $6.726$ \(\Q\) None \(2\) \(-3\) \(-11\) \(-15\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-11q^{5}-6q^{6}+\cdots\)
114.4.a.e 114.a 1.a $2$ $6.726$ \(\Q(\sqrt{17}) \) None \(4\) \(-6\) \(18\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(9+\beta )q^{5}-6q^{6}+\cdots\)
114.4.a.f 114.a 1.a $2$ $6.726$ \(\Q(\sqrt{273}) \) None \(4\) \(6\) \(11\) \(9\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(6-\beta )q^{5}+6q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(114))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(114)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 2}\)