Properties

Label 50.18
Level 50
Weight 18
Dimension 392
Nonzero newspaces 4
Sturm bound 2700
Trace bound 3

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Defining parameters

Level: \( N \) = \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) = \( 18 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(2700\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(50))\).

Total New Old
Modular forms 1303 392 911
Cusp forms 1247 392 855
Eisenstein series 56 0 56

Trace form

\( 392 q - 256 q^{2} - 8324 q^{3} - 65536 q^{4} + 361075 q^{5} - 7980032 q^{6} - 31883368 q^{7} - 16777216 q^{8} + 109313747 q^{9} - 80528640 q^{10} - 204479436 q^{11} - 545521664 q^{12} + 17058885746 q^{13}+ \cdots + 19\!\cdots\!04 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(50))\)

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
50.18.a \(\chi_{50}(1, \cdot)\) 50.18.a.a 1 1
50.18.a.b 1
50.18.a.c 2
50.18.a.d 2
50.18.a.e 2
50.18.a.f 2
50.18.a.g 2
50.18.a.h 3
50.18.a.i 3
50.18.a.j 4
50.18.a.k 4
50.18.b \(\chi_{50}(49, \cdot)\) 50.18.b.a 2 1
50.18.b.b 2
50.18.b.c 4
50.18.b.d 4
50.18.b.e 4
50.18.b.f 4
50.18.b.g 6
50.18.d \(\chi_{50}(11, \cdot)\) n/a 172 4
50.18.e \(\chi_{50}(9, \cdot)\) n/a 168 4

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

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(50))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(50)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)