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Properties

Label 118.6.a
Level $118$
Weight $6$
Character orbit 118.a
Rep. character $\chi_{118}(1,\cdot)$
Character field $\Q$
Dimension $25$
Newform subspaces $4$
Sturm bound $90$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 118 = 2 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 118.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(90\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(118))\).

Total New Old
Modular forms 77 25 52
Cusp forms 73 25 48
Eisenstein series 4 0 4

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

\(2\)\(59\)FrickeDim
\(+\)\(+\)$+$\(6\)
\(+\)\(-\)$-$\(6\)
\(-\)\(+\)$-$\(8\)
\(-\)\(-\)$+$\(5\)
Plus space\(+\)\(11\)
Minus space\(-\)\(14\)

Trace form

\( 25 q + 4 q^{2} - 18 q^{3} + 400 q^{4} - 116 q^{5} + 80 q^{6} - 76 q^{7} + 64 q^{8} + 2127 q^{9} + O(q^{10}) \) \( 25 q + 4 q^{2} - 18 q^{3} + 400 q^{4} - 116 q^{5} + 80 q^{6} - 76 q^{7} + 64 q^{8} + 2127 q^{9} - 296 q^{10} + 1076 q^{11} - 288 q^{12} - 66 q^{13} + 80 q^{14} + 1906 q^{15} + 6400 q^{16} - 2608 q^{17} + 628 q^{18} - 970 q^{19} - 1856 q^{20} + 1494 q^{21} - 2856 q^{22} + 200 q^{23} + 1280 q^{24} + 23849 q^{25} - 880 q^{26} - 13638 q^{27} - 1216 q^{28} - 6240 q^{29} - 2512 q^{30} + 4212 q^{31} + 1024 q^{32} + 21928 q^{33} + 1320 q^{34} - 5978 q^{35} + 34032 q^{36} - 22742 q^{37} + 23392 q^{38} + 7136 q^{39} - 4736 q^{40} - 18182 q^{41} + 12720 q^{42} - 20120 q^{43} + 17216 q^{44} - 6674 q^{45} - 13952 q^{46} + 28676 q^{47} - 4608 q^{48} + 50829 q^{49} + 6556 q^{50} - 9032 q^{51} - 1056 q^{52} - 49816 q^{53} - 6880 q^{54} + 76740 q^{55} + 1280 q^{56} + 82366 q^{57} - 41592 q^{58} - 10443 q^{59} + 30496 q^{60} - 15902 q^{61} + 46080 q^{62} - 114594 q^{63} + 102400 q^{64} - 55344 q^{65} + 9248 q^{66} - 2836 q^{67} - 41728 q^{68} - 115004 q^{69} + 27216 q^{70} + 172026 q^{71} + 10048 q^{72} + 146230 q^{73} + 3856 q^{74} - 214784 q^{75} - 15520 q^{76} - 136128 q^{77} + 104640 q^{78} - 326532 q^{79} - 29696 q^{80} - 63879 q^{81} + 51304 q^{82} + 6820 q^{83} + 23904 q^{84} - 208512 q^{85} - 267656 q^{86} + 57942 q^{87} - 45696 q^{88} - 68190 q^{89} - 53240 q^{90} + 33920 q^{91} + 3200 q^{92} + 248156 q^{93} + 66640 q^{94} - 222622 q^{95} + 20480 q^{96} - 123966 q^{97} + 41284 q^{98} - 237100 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(118))\) 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 59
118.6.a.a 118.a 1.a $5$ $18.925$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(20\) \(-22\) \(-110\) \(-210\) $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+(-4-\beta _{2}-\beta _{4})q^{3}+2^{4}q^{4}+\cdots\)
118.6.a.b 118.a 1.a $6$ $18.925$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-24\) \(-23\) \(-73\) \(25\) $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+(-4+\beta _{1})q^{3}+2^{4}q^{4}+(-12+\cdots)q^{5}+\cdots\)
118.6.a.c 118.a 1.a $6$ $18.925$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-24\) \(4\) \(52\) \(-73\) $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+(1-\beta _{1})q^{3}+2^{4}q^{4}+(8+\beta _{2}+\cdots)q^{5}+\cdots\)
118.6.a.d 118.a 1.a $8$ $18.925$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(32\) \(23\) \(15\) \(182\) $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+(3-\beta _{1})q^{3}+2^{4}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(118))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(118)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 2}\)