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Properties

Label 196.6
Level 196
Weight 6
Dimension 3243
Nonzero newspaces 8
Sturm bound 14112
Trace bound 1

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Defining parameters

Level: \( N \) = \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(14112\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(196))\).

Total New Old
Modular forms 6030 3339 2691
Cusp forms 5730 3243 2487
Eisenstein series 300 96 204

Trace form

\( 3243 q - 15 q^{2} + 6 q^{3} - 15 q^{4} + 90 q^{5} - 21 q^{6} + 116 q^{7} - 561 q^{8} + 363 q^{9} + O(q^{10}) \) \( 3243 q - 15 q^{2} + 6 q^{3} - 15 q^{4} + 90 q^{5} - 21 q^{6} + 116 q^{7} - 561 q^{8} + 363 q^{9} + 1587 q^{10} + 6 q^{11} - 3285 q^{12} + 148 q^{13} - 1878 q^{14} - 5412 q^{15} + 2265 q^{16} + 2214 q^{17} + 13473 q^{18} + 6610 q^{19} - 21 q^{20} + 7779 q^{21} - 26451 q^{22} - 474 q^{23} - 1149 q^{24} - 14599 q^{25} + 17763 q^{26} - 37764 q^{27} + 16806 q^{28} - 29328 q^{29} - 10749 q^{30} - 182 q^{31} - 16815 q^{32} + 93288 q^{33} - 21 q^{34} + 41145 q^{35} + 19983 q^{36} - 47698 q^{37} + 11283 q^{38} - 29649 q^{39} - 70125 q^{40} - 28494 q^{41} - 30777 q^{42} - 58430 q^{43} - 40209 q^{44} - 92667 q^{45} - 32505 q^{46} + 34836 q^{47} - 112558 q^{49} + 159042 q^{50} - 11142 q^{51} + 123531 q^{52} - 58884 q^{53} + 61971 q^{54} - 69609 q^{55} - 27750 q^{56} + 114144 q^{57} + 225447 q^{58} + 251508 q^{59} + 237339 q^{60} + 210215 q^{61} - 21 q^{62} - 168018 q^{63} - 199929 q^{64} - 150378 q^{65} - 443637 q^{66} - 290570 q^{67} - 50061 q^{68} - 420702 q^{69} - 160509 q^{70} - 157752 q^{71} - 518823 q^{72} + 384190 q^{73} - 535761 q^{74} + 450372 q^{75} - 21 q^{76} + 176463 q^{77} + 573033 q^{78} + 263854 q^{79} + 1849770 q^{80} - 9063 q^{81} + 993546 q^{82} - 411048 q^{83} - 1036350 q^{84} - 1022514 q^{85} - 799992 q^{86} - 1292124 q^{87} - 1237290 q^{88} - 188238 q^{89} - 1088892 q^{90} + 23164 q^{91} - 256164 q^{92} + 1808628 q^{93} + 485634 q^{94} + 1318722 q^{95} + 1064160 q^{96} + 339502 q^{97} + 1909020 q^{98} + 846396 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(196))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
196.6.a \(\chi_{196}(1, \cdot)\) 196.6.a.a 1 1
196.6.a.b 1
196.6.a.c 1
196.6.a.d 1
196.6.a.e 1
196.6.a.f 1
196.6.a.g 1
196.6.a.h 2
196.6.a.i 2
196.6.a.j 2
196.6.a.k 4
196.6.d \(\chi_{196}(195, \cdot)\) 196.6.d.a 4 1
196.6.d.b 36
196.6.d.c 56
196.6.e \(\chi_{196}(165, \cdot)\) 196.6.e.a 2 2
196.6.e.b 2
196.6.e.c 2
196.6.e.d 2
196.6.e.e 2
196.6.e.f 2
196.6.e.g 2
196.6.e.h 2
196.6.e.i 2
196.6.e.j 4
196.6.e.k 4
196.6.e.l 8
196.6.f \(\chi_{196}(19, \cdot)\) n/a 192 2
196.6.i \(\chi_{196}(29, \cdot)\) n/a 144 6
196.6.j \(\chi_{196}(27, \cdot)\) n/a 828 6
196.6.m \(\chi_{196}(9, \cdot)\) n/a 276 12
196.6.p \(\chi_{196}(3, \cdot)\) n/a 1656 12

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(196))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(196)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)