Properties

Label 50.26
Level 50
Weight 26
Dimension 578
Nonzero newspaces 4
Sturm bound 3900
Trace bound 1

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Defining parameters

Level: \( N \) = \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) = \( 26 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(3900\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_1(50))\).

Total New Old
Modular forms 1903 578 1325
Cusp forms 1847 578 1269
Eisenstein series 56 0 56

Trace form

\( 578 q - 4096 q^{2} - 1778204 q^{3} + 16777216 q^{4} - 348522485 q^{5} + 10001170432 q^{6} + 182135109512 q^{7} - 68719476736 q^{8} - 7522075206547 q^{9} - 2278810603520 q^{10} - 49180094919444 q^{11} - 29833312600064 q^{12}+ \cdots - 42\!\cdots\!84 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_1(50))\)

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
50.26.a \(\chi_{50}(1, \cdot)\) 50.26.a.a 1 1
50.26.a.b 1
50.26.a.c 2
50.26.a.d 2
50.26.a.e 2
50.26.a.f 2
50.26.a.g 4
50.26.a.h 4
50.26.a.i 5
50.26.a.j 5
50.26.a.k 6
50.26.a.l 6
50.26.b \(\chi_{50}(49, \cdot)\) 50.26.b.a 2 1
50.26.b.b 2
50.26.b.c 4
50.26.b.d 4
50.26.b.e 4
50.26.b.f 4
50.26.b.g 8
50.26.b.h 10
50.26.d \(\chi_{50}(11, \cdot)\) n/a 252 4
50.26.e \(\chi_{50}(9, \cdot)\) n/a 248 4

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

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_1(50))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_1(50)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)