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Properties

Label 197.10.a
Level $197$
Weight $10$
Character orbit 197.a
Rep. character $\chi_{197}(1,\cdot)$
Character field $\Q$
Dimension $147$
Newform subspaces $2$
Sturm bound $165$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 197.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(165\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(197))\).

Total New Old
Modular forms 149 147 2
Cusp forms 147 147 0
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
\(+\)\(71\)
\(-\)\(76\)

Trace form

\( 147 q + 16 q^{2} - 2 q^{3} + 37632 q^{4} + 2842 q^{5} - 7584 q^{6} + 1140 q^{7} + 11574 q^{8} + 938221 q^{9} + O(q^{10}) \) \( 147 q + 16 q^{2} - 2 q^{3} + 37632 q^{4} + 2842 q^{5} - 7584 q^{6} + 1140 q^{7} + 11574 q^{8} + 938221 q^{9} - 17814 q^{10} - 22610 q^{11} - 80896 q^{12} + 46310 q^{13} + 200706 q^{14} - 125252 q^{15} + 9633792 q^{16} + 715870 q^{17} + 343490 q^{18} - 1103338 q^{19} + 715478 q^{20} - 1333544 q^{21} - 1317886 q^{22} + 3562216 q^{23} - 5954214 q^{24} + 54489163 q^{25} - 814756 q^{26} + 2006164 q^{27} - 7390148 q^{28} + 5286264 q^{29} + 15382166 q^{30} + 594442 q^{31} - 2985496 q^{32} + 4918636 q^{33} + 195588 q^{34} - 9474028 q^{35} + 227278196 q^{36} - 547708 q^{37} + 53847140 q^{38} - 78661768 q^{39} + 60029532 q^{40} - 26533502 q^{41} + 52412006 q^{42} + 66230854 q^{43} - 51186588 q^{44} + 163977798 q^{45} + 108966362 q^{46} - 76738004 q^{47} - 154639484 q^{48} + 808307735 q^{49} + 94332844 q^{50} + 75470668 q^{51} - 77679798 q^{52} - 46332360 q^{53} + 40122246 q^{54} + 24319316 q^{55} - 117568648 q^{56} + 224193340 q^{57} + 283520674 q^{58} - 100982534 q^{59} - 266068694 q^{60} - 406109492 q^{61} - 86160438 q^{62} + 38236984 q^{63} + 2547350454 q^{64} - 445900280 q^{65} - 77274062 q^{66} + 175962902 q^{67} + 893282020 q^{68} + 799861844 q^{69} + 735836806 q^{70} + 860565838 q^{71} + 172789938 q^{72} + 524963490 q^{73} - 359189628 q^{74} + 457123558 q^{75} - 1875594332 q^{76} - 448513976 q^{77} - 2709389474 q^{78} + 617151738 q^{79} + 407235440 q^{80} + 5368673387 q^{81} - 1620121960 q^{82} - 884548118 q^{83} + 351927418 q^{84} - 1876479824 q^{85} - 1895528074 q^{86} - 376250512 q^{87} - 2390972670 q^{88} - 1910470810 q^{89} - 665483074 q^{90} - 2169473720 q^{91} + 3915451492 q^{92} - 1294333208 q^{93} - 2456364092 q^{94} - 3259036424 q^{95} - 2016254858 q^{96} + 154080246 q^{97} - 690396732 q^{98} + 2350789054 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(197))\) 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
197.10.a.a 197.a 1.a $71$ $101.462$ None 197.10.a.a \(-32\) \(-892\) \(-2329\) \(-37846\) $+$ $\mathrm{SU}(2)$
197.10.a.b 197.a 1.a $76$ $101.462$ None 197.10.a.b \(48\) \(890\) \(5171\) \(38986\) $-$ $\mathrm{SU}(2)$