Properties

Label 78.3
Level 78
Weight 3
Dimension 84
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 1008
Trace bound 4

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Defining parameters

Level: \( N \) = \( 78 = 2 \cdot 3 \cdot 13 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(1008\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(78))\).

Total New Old
Modular forms 384 84 300
Cusp forms 288 84 204
Eisenstein series 96 0 96

Trace form

\( 84 q + 40 q^{7} + 24 q^{8} + 12 q^{9} + 60 q^{10} + 24 q^{11} - 48 q^{13} - 48 q^{14} - 72 q^{15} - 32 q^{16} - 72 q^{17} - 36 q^{18} - 80 q^{19} - 48 q^{20} + 60 q^{21} + 48 q^{23} - 72 q^{27} - 120 q^{29}+ \cdots - 612 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(78))\)

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
78.3.c \(\chi_{78}(53, \cdot)\) 78.3.c.a 8 1
78.3.d \(\chi_{78}(77, \cdot)\) 78.3.d.a 4 1
78.3.d.b 4
78.3.f \(\chi_{78}(31, \cdot)\) 78.3.f.a 4 2
78.3.f.b 8
78.3.h \(\chi_{78}(29, \cdot)\) 78.3.h.a 8 2
78.3.h.b 12
78.3.j \(\chi_{78}(17, \cdot)\) 78.3.j.a 20 2
78.3.l \(\chi_{78}(7, \cdot)\) 78.3.l.a 4 4
78.3.l.b 4
78.3.l.c 8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(78))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(78)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)