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Properties

Label 98.6
Level 98
Weight 6
Dimension 470
Nonzero newspaces 4
Newform subspaces 22
Sturm bound 3528
Trace bound 1

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Defining parameters

Level: \( N \) = \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 22 \)
Sturm bound: \(3528\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(98))\).

Total New Old
Modular forms 1530 470 1060
Cusp forms 1410 470 940
Eisenstein series 120 0 120

Trace form

\( 470 q - 36 q^{3} + 64 q^{4} - 132 q^{5} - 432 q^{6} - 232 q^{7} + 2436 q^{9} + O(q^{10}) \) \( 470 q - 36 q^{3} + 64 q^{4} - 132 q^{5} - 432 q^{6} - 232 q^{7} + 2436 q^{9} + 1488 q^{10} + 888 q^{11} - 576 q^{12} - 7300 q^{13} + 120 q^{14} + 5136 q^{15} + 1024 q^{16} + 6456 q^{17} - 2976 q^{18} - 7036 q^{19} - 4800 q^{20} - 8790 q^{21} - 5664 q^{22} + 4224 q^{23} + 3840 q^{24} + 76 q^{25} + 22704 q^{26} + 48744 q^{27} + 6656 q^{28} + 8496 q^{29} - 12576 q^{30} - 37912 q^{31} - 17688 q^{33} - 27744 q^{34} + 10878 q^{35} - 47040 q^{36} + 89472 q^{37} + 4296 q^{38} - 111030 q^{39} - 59520 q^{40} - 150708 q^{41} - 66600 q^{42} - 4468 q^{43} + 17568 q^{44} + 133626 q^{45} + 106440 q^{46} + 97404 q^{47} + 23040 q^{48} + 320270 q^{49} + 29712 q^{50} + 299520 q^{51} + 50976 q^{52} + 136236 q^{53} - 24984 q^{54} - 457734 q^{55} - 126720 q^{56} - 140508 q^{57} - 282288 q^{58} - 214584 q^{59} - 151776 q^{60} - 88158 q^{61} - 80040 q^{62} + 446844 q^{63} - 81920 q^{64} - 29736 q^{65} + 192000 q^{66} - 131008 q^{67} + 103296 q^{68} + 66672 q^{69} + 131208 q^{70} + 271440 q^{71} - 47616 q^{72} + 92096 q^{73} - 73440 q^{74} - 220620 q^{75} - 53440 q^{76} - 4368 q^{77} - 364032 q^{78} + 165344 q^{79} - 33792 q^{80} + 1037616 q^{81} + 256416 q^{82} - 164376 q^{83} + 69792 q^{84} - 420660 q^{85} - 127392 q^{86} - 1874064 q^{87} + 46080 q^{88} - 367836 q^{89} + 128784 q^{90} + 113446 q^{91} + 76032 q^{92} + 1069092 q^{93} - 94656 q^{94} + 1515336 q^{95} + 61440 q^{96} + 990884 q^{97} + 50016 q^{98} + 114192 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(98))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
98.6.a \(\chi_{98}(1, \cdot)\) 98.6.a.a 1 1
98.6.a.b 1
98.6.a.c 2
98.6.a.d 2
98.6.a.e 2
98.6.a.f 2
98.6.a.g 2
98.6.a.h 2
98.6.a.i 4
98.6.c \(\chi_{98}(67, \cdot)\) 98.6.c.a 2 2
98.6.c.b 2
98.6.c.c 2
98.6.c.d 2
98.6.c.e 4
98.6.c.f 4
98.6.c.g 4
98.6.c.h 4
98.6.c.i 8
98.6.e \(\chi_{98}(15, \cdot)\) 98.6.e.a 66 6
98.6.e.b 66
98.6.g \(\chi_{98}(9, \cdot)\) 98.6.g.a 144 12
98.6.g.b 144

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(98))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(98)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)