Properties

Label 98.10
Level 98
Weight 10
Dimension 847
Nonzero newspaces 4
Newform subspaces 30
Sturm bound 5880
Trace bound 1

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Defining parameters

Level: \( N \) = \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 30 \)
Sturm bound: \(5880\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(98))\).

Total New Old
Modular forms 2706 847 1859
Cusp forms 2586 847 1739
Eisenstein series 120 0 120

Trace form

\( 847q + 16q^{2} + 492q^{3} + 256q^{4} + 4278q^{5} - 18048q^{6} + 2736q^{7} + 4096q^{8} - 96735q^{9} + O(q^{10}) \) \( 847q + 16q^{2} + 492q^{3} + 256q^{4} + 4278q^{5} - 18048q^{6} + 2736q^{7} + 4096q^{8} - 96735q^{9} - 139872q^{10} + 69432q^{11} + 125952q^{12} - 943102q^{13} + 191136q^{14} - 841584q^{15} + 65536q^{16} + 3085926q^{17} + 1474896q^{18} - 2730340q^{19} - 1697280q^{20} - 86784q^{21} + 1144128q^{22} + 13155204q^{23} + 2850816q^{24} + 8488051q^{25} - 5878624q^{26} - 54459288q^{27} - 3190272q^{28} + 29842110q^{29} + 42658944q^{30} + 29292044q^{31} + 1048576q^{32} - 77242836q^{33} - 36034656q^{34} - 33192852q^{35} - 61880064q^{36} - 24940294q^{37} - 8397664q^{38} + 204802836q^{39} + 101990400q^{40} - 76696422q^{41} - 162048672q^{42} - 176148724q^{43} - 135237120q^{44} + 76820826q^{45} + 208078176q^{46} + 295955628q^{47} + 42860544q^{48} + 667508862q^{49} + 316968112q^{50} - 472857444q^{51} - 149542912q^{52} - 841866894q^{53} - 797870880q^{54} - 389435724q^{55} + 148783104q^{56} + 875155008q^{57} + 1238715552q^{58} + 524391876q^{59} - 294437376q^{60} - 2346074554q^{61} - 1257786592q^{62} + 496193088q^{63} - 587202560q^{64} - 298208316q^{65} - 376062720q^{66} - 175946296q^{67} + 789997056q^{68} + 1956429432q^{69} + 604181088q^{70} - 600747048q^{71} + 377573376q^{72} - 2211740458q^{73} - 1240414240q^{74} + 815640600q^{75} + 595355648q^{76} + 1082398506q^{77} - 976447104q^{78} - 3715040932q^{79} + 280363008q^{80} - 4328567067q^{81} + 2523435552q^{82} + 1146090468q^{83} + 1131039744q^{84} + 7477059840q^{85} - 2107480000q^{86} + 1760542512q^{87} + 175325184q^{88} - 4084864950q^{89} - 7375386336q^{90} - 7285583070q^{91} - 3126718464q^{92} - 4641098136q^{93} + 1241988480q^{94} + 4906995636q^{95} + 729808896q^{96} + 17486621270q^{97} + 4245128448q^{98} + 12751598700q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(98))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
98.10.a \(\chi_{98}(1, \cdot)\) 98.10.a.a 1 1
98.10.a.b 1
98.10.a.c 1
98.10.a.d 2
98.10.a.e 2
98.10.a.f 2
98.10.a.g 3
98.10.a.h 3
98.10.a.i 3
98.10.a.j 3
98.10.a.k 4
98.10.a.l 6
98.10.c \(\chi_{98}(67, \cdot)\) 98.10.c.a 2 2
98.10.c.b 2
98.10.c.c 2
98.10.c.d 2
98.10.c.e 2
98.10.c.f 2
98.10.c.g 4
98.10.c.h 4
98.10.c.i 4
98.10.c.j 4
98.10.c.k 6
98.10.c.l 6
98.10.c.m 8
98.10.c.n 12
98.10.e \(\chi_{98}(15, \cdot)\) 98.10.e.a 126 6
98.10.e.b 126
98.10.g \(\chi_{98}(9, \cdot)\) 98.10.g.a 252 12
98.10.g.b 252

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(98))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(98)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)