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Properties

Label 114.8.a
Level $114$
Weight $8$
Character orbit 114.a
Rep. character $\chi_{114}(1,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $10$
Sturm bound $160$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 114.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(160\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(114))\).

Total New Old
Modular forms 144 20 124
Cusp forms 136 20 116
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
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(1\)
Plus space\(+\)\(12\)
Minus space\(-\)\(8\)

Trace form

\( 20 q - 16 q^{2} + 1280 q^{4} + 224 q^{5} - 432 q^{6} + 2136 q^{7} - 1024 q^{8} + 14580 q^{9} + O(q^{10}) \) \( 20 q - 16 q^{2} + 1280 q^{4} + 224 q^{5} - 432 q^{6} + 2136 q^{7} - 1024 q^{8} + 14580 q^{9} + 5824 q^{10} - 12996 q^{11} + 15556 q^{13} - 21276 q^{15} + 81920 q^{16} + 23512 q^{17} - 11664 q^{18} - 13718 q^{19} + 14336 q^{20} - 52832 q^{22} - 67764 q^{23} - 27648 q^{24} + 194620 q^{25} + 142368 q^{26} + 136704 q^{28} - 18140 q^{29} - 108000 q^{30} - 500980 q^{31} - 65536 q^{32} + 210276 q^{33} + 533856 q^{34} + 12144 q^{35} + 933120 q^{36} + 1176572 q^{37} + 505224 q^{39} + 372736 q^{40} + 1179932 q^{41} + 29376 q^{42} - 347104 q^{43} - 831744 q^{44} + 163296 q^{45} + 690304 q^{46} + 3115980 q^{47} - 874244 q^{49} - 1009776 q^{50} + 887328 q^{51} + 995584 q^{52} + 4921516 q^{53} - 314928 q^{54} + 2706416 q^{55} - 370386 q^{57} + 4283840 q^{58} - 2460416 q^{59} - 1361664 q^{60} - 732104 q^{61} - 3179776 q^{62} + 1557144 q^{63} + 5242880 q^{64} + 6856792 q^{65} - 4256928 q^{66} + 2180928 q^{67} + 1504768 q^{68} + 3262680 q^{69} + 13633920 q^{70} - 11573504 q^{71} - 746496 q^{72} - 14190120 q^{73} - 4172576 q^{74} + 3296160 q^{75} - 877952 q^{76} + 8346184 q^{77} - 2552256 q^{78} + 7952524 q^{79} + 917504 q^{80} + 10628820 q^{81} + 19788416 q^{82} + 10739924 q^{83} - 25097208 q^{85} + 4078784 q^{86} - 202932 q^{87} - 3381248 q^{88} - 565724 q^{89} + 4245696 q^{90} - 1949184 q^{91} - 4336896 q^{92} + 10905192 q^{93} - 6674624 q^{94} + 15336724 q^{95} - 1769472 q^{96} + 8825336 q^{97} + 13827440 q^{98} - 9474084 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(114))\) 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 3 19
114.8.a.a 114.a 1.a $1$ $35.612$ \(\Q\) None 114.8.a.a \(-8\) \(-27\) \(-135\) \(71\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}-135q^{5}+\cdots\)
114.8.a.b 114.a 1.a $1$ $35.612$ \(\Q\) None 114.8.a.b \(-8\) \(-27\) \(450\) \(-568\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}+450q^{5}+\cdots\)
114.8.a.c 114.a 1.a $1$ $35.612$ \(\Q\) None 114.8.a.c \(8\) \(-27\) \(-140\) \(-60\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}-140q^{5}+\cdots\)
114.8.a.d 114.a 1.a $1$ $35.612$ \(\Q\) None 114.8.a.d \(8\) \(-27\) \(-47\) \(405\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}-47q^{5}-6^{3}q^{6}+\cdots\)
114.8.a.e 114.a 1.a $1$ $35.612$ \(\Q\) None 114.8.a.e \(8\) \(27\) \(-75\) \(-497\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}-75q^{5}+6^{3}q^{6}+\cdots\)
114.8.a.f 114.a 1.a $3$ $35.612$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 114.8.a.f \(-24\) \(-81\) \(-369\) \(1065\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(-123+\beta _{2})q^{5}+\cdots\)
114.8.a.g 114.a 1.a $3$ $35.612$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 114.8.a.g \(-24\) \(81\) \(-441\) \(345\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(-147-\beta _{1}+\cdots)q^{5}+\cdots\)
114.8.a.h 114.a 1.a $3$ $35.612$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 114.8.a.h \(-24\) \(81\) \(243\) \(155\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(3^{4}+\beta _{1}+\cdots)q^{5}+\cdots\)
114.8.a.i 114.a 1.a $3$ $35.612$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 114.8.a.i \(24\) \(-81\) \(747\) \(155\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(249+\beta _{1}+\cdots)q^{5}+\cdots\)
114.8.a.j 114.a 1.a $3$ $35.612$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 114.8.a.j \(24\) \(81\) \(-9\) \(1065\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(-3+\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(114))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(114)) \simeq \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 2}\)