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Properties

Label 98.5
Level 98
Weight 5
Dimension 376
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 2940
Trace bound 1

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Defining parameters

Level: \( N \) = \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(2940\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(98))\).

Total New Old
Modular forms 1236 376 860
Cusp forms 1116 376 740
Eisenstein series 120 0 120

Trace form

\( 376 q + 36 q^{3} - 32 q^{4} - 108 q^{5} + 104 q^{7} + 336 q^{9} + O(q^{10}) \) \( 376 q + 36 q^{3} - 32 q^{4} - 108 q^{5} + 104 q^{7} + 336 q^{9} + 192 q^{10} - 612 q^{11} - 288 q^{12} + 288 q^{14} + 648 q^{15} - 256 q^{16} - 1836 q^{17} - 1536 q^{18} - 60 q^{19} - 390 q^{21} + 1920 q^{22} + 2556 q^{23} + 1536 q^{24} + 5744 q^{25} + 3456 q^{26} - 848 q^{28} - 8928 q^{29} - 11136 q^{30} + 1092 q^{31} - 2124 q^{33} - 2142 q^{35} + 6720 q^{36} - 20268 q^{37} - 1440 q^{38} + 5514 q^{39} + 3840 q^{40} + 19404 q^{41} + 23616 q^{42} + 13556 q^{43} + 7200 q^{44} + 39582 q^{45} + 8352 q^{46} + 6408 q^{47} - 5552 q^{49} + 5760 q^{50} - 25236 q^{51} - 4160 q^{52} - 51192 q^{53} - 51552 q^{54} - 89670 q^{55} - 13824 q^{56} - 15756 q^{57} - 28800 q^{58} - 21960 q^{59} + 288 q^{60} + 44506 q^{61} + 42336 q^{62} + 73632 q^{63} - 8192 q^{64} + 14112 q^{65} + 6912 q^{66} + 12220 q^{67} + 14688 q^{68} + 3360 q^{70} + 5472 q^{71} - 12288 q^{72} + 34548 q^{73} + 15552 q^{74} + 10440 q^{75} - 8442 q^{77} - 27264 q^{78} - 27140 q^{79} + 6912 q^{80} - 58404 q^{81} - 19968 q^{82} - 35280 q^{83} - 1104 q^{84} - 27576 q^{85} + 43776 q^{86} + 148872 q^{87} + 19968 q^{88} + 101556 q^{89} + 65328 q^{91} - 2880 q^{92} + 57492 q^{93} - 30336 q^{94} - 29052 q^{95} - 12288 q^{96} - 21888 q^{98} + 16896 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(98))\)

We only show spaces with odd 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
98.5.b \(\chi_{98}(97, \cdot)\) 98.5.b.a 4 1
98.5.b.b 4
98.5.b.c 4
98.5.d \(\chi_{98}(19, \cdot)\) 98.5.d.a 4 2
98.5.d.b 8
98.5.d.c 8
98.5.d.d 8
98.5.f \(\chi_{98}(13, \cdot)\) 98.5.f.a 120 6
98.5.h \(\chi_{98}(3, \cdot)\) 98.5.h.a 216 12

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(98))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(98)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)