Properties

Label 50.28
Level 50
Weight 28
Dimension 623
Nonzero newspaces 4
Sturm bound 4200
Trace bound 1

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Defining parameters

Level: \( N \) = \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) = \( 28 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(4200\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{28}(\Gamma_1(50))\).

Total New Old
Modular forms 2053 623 1430
Cusp forms 1997 623 1374
Eisenstein series 56 0 56

Trace form

\( 623 q - 16384 q^{2} + 2265736 q^{3} + 268435456 q^{4} + 5046027125 q^{5} - 772210688 q^{6} - 899335433352 q^{7} - 1099511627776 q^{8} + 34830479514308 q^{9} + 27025798389760 q^{10} + 381479843219776 q^{11}+ \cdots + 23\!\cdots\!36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{28}^{\mathrm{new}}(\Gamma_1(50))\)

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
50.28.a \(\chi_{50}(1, \cdot)\) 50.28.a.a 1 1
50.28.a.b 1
50.28.a.c 2
50.28.a.d 2
50.28.a.e 2
50.28.a.f 3
50.28.a.g 4
50.28.a.h 4
50.28.a.i 5
50.28.a.j 5
50.28.a.k 7
50.28.a.l 7
50.28.b \(\chi_{50}(49, \cdot)\) 50.28.b.a 2 1
50.28.b.b 2
50.28.b.c 4
50.28.b.d 4
50.28.b.e 4
50.28.b.f 6
50.28.b.g 8
50.28.b.h 10
50.28.d \(\chi_{50}(11, \cdot)\) n/a 268 4
50.28.e \(\chi_{50}(9, \cdot)\) n/a 272 4

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

Decomposition of \(S_{28}^{\mathrm{old}}(\Gamma_1(50))\) into lower level spaces

\( S_{28}^{\mathrm{old}}(\Gamma_1(50)) \cong \) \(S_{28}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)