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Properties

Label 197.4.g
Level $197$
Weight $4$
Character orbit 197.g
Rep. character $\chi_{197}(16,\cdot)$
Character field $\Q(\zeta_{49})$
Dimension $2058$
Newform subspaces $1$
Sturm bound $66$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 197.g (of order \(49\) and degree \(42\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 197 \)
Character field: \(\Q(\zeta_{49})\)
Newform subspaces: \( 1 \)
Sturm bound: \(66\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(197, [\chi])\).

Total New Old
Modular forms 2142 2142 0
Cusp forms 2058 2058 0
Eisenstein series 84 84 0

Trace form

\( 2058 q - 42 q^{2} - 42 q^{3} - 84 q^{4} - 42 q^{5} - 119 q^{6} - 84 q^{7} - 98 q^{8} - 42 q^{9} + O(q^{10}) \) \( 2058 q - 42 q^{2} - 42 q^{3} - 84 q^{4} - 42 q^{5} - 119 q^{6} - 84 q^{7} - 98 q^{8} - 42 q^{9} + 168 q^{10} - 140 q^{11} + 14 q^{12} - 42 q^{13} - 812 q^{14} + 1638 q^{15} + 672 q^{16} - 42 q^{17} + 147 q^{18} - 567 q^{19} - 35 q^{20} - 42 q^{21} + 1302 q^{22} - 42 q^{23} - 434 q^{24} - 42 q^{25} + 364 q^{26} - 1596 q^{27} - 147 q^{28} + 4676 q^{29} - 847 q^{30} + 882 q^{31} + 910 q^{32} - 287 q^{33} - 882 q^{34} - 42 q^{35} - 17787 q^{36} - 1400 q^{37} + 14 q^{38} + 168 q^{39} + 3962 q^{40} - 392 q^{41} + 1764 q^{42} + 294 q^{43} - 12978 q^{44} + 2814 q^{45} + 840 q^{46} + 28 q^{47} + 3654 q^{48} + 1554 q^{49} - 4998 q^{50} - 98 q^{51} - 3703 q^{52} - 42 q^{53} - 1365 q^{54} + 4046 q^{55} - 3073 q^{56} + 14567 q^{57} - 10402 q^{58} + 4004 q^{59} - 4536 q^{60} - 1050 q^{61} + 210 q^{62} + 2254 q^{63} + 3822 q^{64} - 1106 q^{65} - 875 q^{66} - 3612 q^{67} + 819 q^{68} + 4333 q^{69} - 5292 q^{70} + 11424 q^{71} - 1876 q^{72} - 714 q^{73} + 1288 q^{74} - 1316 q^{75} + 8715 q^{76} + 6629 q^{77} + 13986 q^{78} - 1512 q^{79} + 406 q^{80} + 1078 q^{81} - 42 q^{82} - 5999 q^{83} - 7595 q^{84} + 30492 q^{85} + 7749 q^{86} - 35 q^{87} + 8897 q^{88} - 196 q^{89} - 14910 q^{90} - 8232 q^{91} - 7938 q^{92} - 2639 q^{93} - 11116 q^{94} + 3703 q^{95} + 14497 q^{96} - 2674 q^{97} - 10024 q^{98} + 6237 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(197, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
197.4.g.a 197.g 197.g $2058$ $11.623$ None 197.4.g.a \(-42\) \(-42\) \(-42\) \(-84\) $\mathrm{SU}(2)[C_{49}]$