Properties

Label 197.12.a
Level $197$
Weight $12$
Character orbit 197.a
Rep. character $\chi_{197}(1,\cdot)$
Character field $\Q$
Dimension $179$
Newform subspaces $2$
Sturm bound $198$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 197.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(198\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(197))\).

Total New Old
Modular forms 183 179 4
Cusp forms 181 179 2
Eisenstein series 2 0 2

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

\(197\)Dim
\(+\)\(92\)
\(-\)\(87\)

Trace form

\( 179 q - 32 q^{2} - 506 q^{3} + 181248 q^{4} - 4292 q^{5} + 15552 q^{6} + 73958 q^{7} - 23466 q^{8} + 10915153 q^{9} + O(q^{10}) \) \( 179 q - 32 q^{2} - 506 q^{3} + 181248 q^{4} - 4292 q^{5} + 15552 q^{6} + 73958 q^{7} - 23466 q^{8} + 10915153 q^{9} - 451446 q^{10} - 1707062 q^{11} - 1036288 q^{12} + 3046244 q^{13} + 3377650 q^{14} - 4726682 q^{15} + 181403648 q^{16} - 138632 q^{17} - 16589758 q^{18} + 4338482 q^{19} + 44409558 q^{20} + 46136452 q^{21} + 44896562 q^{22} - 77277104 q^{23} - 30847446 q^{24} + 1738156885 q^{25} - 62733812 q^{26} + 67920886 q^{27} + 49491820 q^{28} - 251788870 q^{29} - 474827530 q^{30} + 161802396 q^{31} + 272554840 q^{32} + 78935140 q^{33} - 144713724 q^{34} + 215781724 q^{35} + 10506506996 q^{36} - 142573880 q^{37} - 857822124 q^{38} + 2394560438 q^{39} - 1799514708 q^{40} - 2377153492 q^{41} + 1614214262 q^{42} + 880054814 q^{43} + 101369540 q^{44} + 4773894 q^{45} + 451010202 q^{46} - 5301347590 q^{47} + 8809371172 q^{48} + 50524045501 q^{49} - 10601888772 q^{50} - 3162536174 q^{51} + 18317913802 q^{52} + 119766580 q^{53} - 4972778874 q^{54} + 9434182794 q^{55} + 35328186936 q^{56} - 10571741984 q^{57} - 4007942798 q^{58} + 16187715582 q^{59} + 6009852298 q^{60} - 14465398644 q^{61} - 43463472262 q^{62} + 15168448702 q^{63} + 162486953526 q^{64} + 2232825030 q^{65} - 19819831838 q^{66} + 47254686328 q^{67} + 25121875156 q^{68} - 74474183392 q^{69} + 24041413558 q^{70} + 14752009558 q^{71} + 84397626210 q^{72} - 34758371608 q^{73} - 95262925132 q^{74} + 6656822788 q^{75} + 55547915476 q^{76} - 1898299652 q^{77} + 31518277918 q^{78} + 29767846366 q^{79} + 115197283696 q^{80} + 635447630747 q^{81} + 70344065848 q^{82} + 164969853872 q^{83} + 147596010202 q^{84} - 8103076680 q^{85} + 197759629654 q^{86} + 99578816480 q^{87} + 265449026946 q^{88} + 53135278642 q^{89} - 478903734130 q^{90} - 37783882660 q^{91} - 421620319388 q^{92} + 269832424126 q^{93} - 246616469772 q^{94} - 45076718962 q^{95} - 167130334250 q^{96} - 12329623248 q^{97} - 23184330508 q^{98} - 228362184182 q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(197))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 197
197.12.a.a 197.a 1.a $87$ $151.364$ None 197.12.a.a \(-96\) \(-2926\) \(-20896\) \(-231933\) $-$ $\mathrm{SU}(2)$
197.12.a.b 197.a 1.a $92$ $151.364$ None 197.12.a.b \(64\) \(2420\) \(16604\) \(305891\) $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(197))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(197)) \simeq \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)