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

\( 470 q - 36 q^{3} + 64 q^{4} - 132 q^{5} - 432 q^{6} - 232 q^{7} + 2436 q^{9} + 1488 q^{10} + 888 q^{11} - 576 q^{12} - 7300 q^{13} + 120 q^{14} + 5136 q^{15} + 1024 q^{16} + 6456 q^{17} - 2976 q^{18} - 7036 q^{19}+ \cdots + 114192 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

\( S_{6}^{\mathrm{old}}(\Gamma_1(98)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)