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Properties

Label 197.14.a
Level $197$
Weight $14$
Character orbit 197.a
Rep. character $\chi_{197}(1,\cdot)$
Character field $\Q$
Dimension $213$
Newform subspaces $2$
Sturm bound $231$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 197.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(231\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(197))\).

Total New Old
Modular forms 215 213 2
Cusp forms 213 213 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
\(+\)\(104\)
\(-\)\(109\)

Trace form

\( 213 q + 64 q^{2} - 2 q^{3} + 880640 q^{4} - 10508 q^{5} + 299904 q^{6} - 403306 q^{7} - 290442 q^{8} + 111071167 q^{9} + O(q^{10}) \) \( 213 q + 64 q^{2} - 2 q^{3} + 880640 q^{4} - 10508 q^{5} + 299904 q^{6} - 403306 q^{7} - 290442 q^{8} + 111071167 q^{9} + 6747306 q^{10} + 10510498 q^{11} - 4931584 q^{12} - 35067412 q^{13} - 14577374 q^{14} - 98882522 q^{15} + 3674210304 q^{16} + 118781464 q^{17} - 49010926 q^{18} - 355966726 q^{19} - 84061482 q^{20} - 292293140 q^{21} - 1081805054 q^{22} - 1712247728 q^{23} + 5351789946 q^{24} + 53938480123 q^{25} - 596088644 q^{26} + 1557918478 q^{27} + 2275553820 q^{28} + 7232993390 q^{29} - 7563496234 q^{30} + 3700964284 q^{31} - 20911534520 q^{32} - 22743610820 q^{33} - 1550192412 q^{34} - 961430228 q^{35} + 477982208372 q^{36} - 10895743560 q^{37} + 33184592772 q^{38} + 5453286662 q^{39} + 18881742972 q^{40} + 43276377284 q^{41} - 80174787514 q^{42} - 10620751642 q^{43} - 133504177372 q^{44} + 16660153458 q^{45} - 57910920102 q^{46} + 99590810330 q^{47} - 251835700796 q^{48} + 2850374555771 q^{49} + 164291940924 q^{50} - 262674261398 q^{51} - 234926037174 q^{52} + 504468579580 q^{53} + 1081242585222 q^{54} - 498675903174 q^{55} - 980368023816 q^{56} + 238688003488 q^{57} + 55490658914 q^{58} + 51914853510 q^{59} - 2304732128534 q^{60} + 951426418852 q^{61} + 2618909324714 q^{62} - 2560924922306 q^{63} + 16282595907254 q^{64} - 37148268870 q^{65} + 7860885141778 q^{66} + 724667994024 q^{67} - 171108760508 q^{68} + 3136464958304 q^{69} - 2804901282394 q^{70} - 1188579531482 q^{71} - 8726729616750 q^{72} + 2111345205224 q^{73} + 5821521205124 q^{74} - 7712925574172 q^{75} - 4971403165308 q^{76} - 3142226117036 q^{77} - 1560438154274 q^{78} - 1389457688898 q^{79} - 1564512175760 q^{80} + 54216024955229 q^{81} + 5833702556024 q^{82} - 5264184894976 q^{83} + 3017684123962 q^{84} + 9639901623336 q^{85} + 9750267489142 q^{86} + 11707978292000 q^{87} - 17835580413438 q^{88} + 6643190964430 q^{89} + 30548206924766 q^{90} + 24490130487180 q^{91} - 38647820050844 q^{92} - 15026998386278 q^{93} + 33691305982308 q^{94} + 12042669661646 q^{95} + 50450362127926 q^{96} + 3670692673696 q^{97} - 15983307150796 q^{98} + 3417936671410 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(197))\) 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
197.14.a.a 197.a 1.a $104$ $211.245$ None 197.14.a.a \(-128\) \(-8020\) \(-99004\) \(-2084037\) $+$ $\mathrm{SU}(2)$
197.14.a.b 197.a 1.a $109$ $211.245$ None 197.14.a.b \(192\) \(8018\) \(88496\) \(1680731\) $-$ $\mathrm{SU}(2)$