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

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

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

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