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Properties

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

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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

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

Display 100 coefficients 10 coefficients

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

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