Properties

Label 98.4
Level 98
Weight 4
Dimension 282
Nonzero newspaces 4
Newform subspaces 20
Sturm bound 2352
Trace bound 1

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 20 \)
Sturm bound: \(2352\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(98))\).

Total New Old
Modular forms 942 282 660
Cusp forms 822 282 540
Eisenstein series 120 0 120

Trace form

\( 282q - 24q^{3} + 48q^{5} + 72q^{6} + 48q^{7} - 84q^{9} + O(q^{10}) \) \( 282q - 24q^{3} + 48q^{5} + 72q^{6} + 48q^{7} - 84q^{9} - 72q^{10} - 84q^{11} - 96q^{12} - 132q^{13} - 132q^{14} + 24q^{15} + 300q^{17} + 336q^{18} + 120q^{19} + 240q^{20} + 72q^{21} + 432q^{22} + 588q^{23} + 96q^{24} - 420q^{25} - 696q^{26} - 1152q^{27} - 120q^{28} - 1152q^{29} - 336q^{30} - 420q^{31} + 1140q^{33} + 816q^{34} + 420q^{35} + 336q^{36} + 4620q^{37} + 2388q^{38} + 4620q^{39} + 720q^{40} + 2256q^{41} - 828q^{42} - 480q^{43} - 1512q^{44} - 7404q^{45} - 4956q^{46} - 3828q^{47} - 480q^{48} - 7974q^{49} - 3912q^{50} - 9324q^{51} - 1128q^{52} - 4956q^{53} - 1980q^{54} - 3924q^{55} + 288q^{56} + 1392q^{57} + 4536q^{58} + 5736q^{59} + 4536q^{60} + 8904q^{61} + 5388q^{62} + 9120q^{63} - 768q^{64} + 4032q^{65} + 768q^{66} + 4116q^{67} + 1200q^{68} + 2664q^{69} + 756q^{70} + 1584q^{71} + 1344q^{72} + 1188q^{73} - 3024q^{74} - 468q^{75} - 2928q^{76} - 2226q^{77} - 2304q^{78} - 2100q^{79} + 768q^{80} + 14532q^{81} + 1968q^{82} + 9504q^{83} + 912q^{84} + 4476q^{85} - 1680q^{86} - 2424q^{87} - 2688q^{88} - 6720q^{89} - 4776q^{90} - 5526q^{91} + 864q^{92} - 19992q^{93} + 1632q^{94} - 11172q^{95} + 384q^{96} + 300q^{97} + 2640q^{98} - 8496q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(98))\)

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
98.4.a \(\chi_{98}(1, \cdot)\) 98.4.a.a 1 1
98.4.a.b 1
98.4.a.c 1
98.4.a.d 1
98.4.a.e 1
98.4.a.f 1
98.4.a.g 2
98.4.a.h 2
98.4.c \(\chi_{98}(67, \cdot)\) 98.4.c.a 2 2
98.4.c.b 2
98.4.c.c 2
98.4.c.d 2
98.4.c.e 2
98.4.c.f 2
98.4.c.g 4
98.4.c.h 4
98.4.e \(\chi_{98}(15, \cdot)\) 98.4.e.a 42 6
98.4.e.b 42
98.4.g \(\chi_{98}(9, \cdot)\) 98.4.g.a 84 12
98.4.g.b 84

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(98))\) into lower level spaces

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