Properties

Label 676.6
Level 676
Weight 6
Dimension 40712
Nonzero newspaces 12
Sturm bound 170352
Trace bound 3

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Defining parameters

Level: \( N \) = \( 676 = 2^{2} \cdot 13^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(170352\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(676))\).

Total New Old
Modular forms 71550 41120 30430
Cusp forms 70410 40712 29698
Eisenstein series 1140 408 732

Trace form

\( 40712 q - 66 q^{2} - 12 q^{3} - 66 q^{4} - 78 q^{5} - 66 q^{6} + 508 q^{7} - 66 q^{8} - 1527 q^{9} - 66 q^{10} + 1608 q^{11} - 78 q^{12} + 1428 q^{13} - 126 q^{14} - 3024 q^{15} - 66 q^{16} - 10596 q^{17}+ \cdots - 337896 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(676))\)

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
676.6.a \(\chi_{676}(1, \cdot)\) 676.6.a.a 1 1
676.6.a.b 1
676.6.a.c 1
676.6.a.d 3
676.6.a.e 6
676.6.a.f 6
676.6.a.g 6
676.6.a.h 10
676.6.a.i 15
676.6.a.j 15
676.6.d \(\chi_{676}(337, \cdot)\) 676.6.d.a 2 1
676.6.d.b 2
676.6.d.c 2
676.6.d.d 6
676.6.d.e 10
676.6.d.f 12
676.6.d.g 30
676.6.e \(\chi_{676}(529, \cdot)\) n/a 128 2
676.6.f \(\chi_{676}(99, \cdot)\) n/a 750 2
676.6.h \(\chi_{676}(361, \cdot)\) n/a 130 2
676.6.l \(\chi_{676}(19, \cdot)\) n/a 1500 4
676.6.m \(\chi_{676}(53, \cdot)\) n/a 924 12
676.6.n \(\chi_{676}(25, \cdot)\) n/a 912 12
676.6.q \(\chi_{676}(9, \cdot)\) n/a 1824 24
676.6.s \(\chi_{676}(31, \cdot)\) n/a 10872 24
676.6.v \(\chi_{676}(17, \cdot)\) n/a 1800 24
676.6.w \(\chi_{676}(7, \cdot)\) n/a 21744 48

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(676))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(676)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 2}\)