Properties

Label 64.22
Level 64
Weight 22
Dimension 1501
Nonzero newspaces 4
Sturm bound 5632
Trace bound 1

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Defining parameters

Level: \( N \) = \( 64 = 2^{6} \)
Weight: \( k \) = \( 22 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(5632\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(64))\).

Total New Old
Modular forms 2724 1523 1201
Cusp forms 2652 1501 1151
Eisenstein series 72 22 50

Trace form

\( 1501 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 10460353213 q^{9} - 8 q^{10} - 67333320746 q^{11} - 8 q^{12} - 1065395863664 q^{13} - 8 q^{14} - 4613203125004 q^{15} - 8 q^{16}+ \cdots - 27\!\cdots\!22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(64))\)

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
64.22.a \(\chi_{64}(1, \cdot)\) 64.22.a.a 1 1
64.22.a.b 1
64.22.a.c 1
64.22.a.d 1
64.22.a.e 1
64.22.a.f 1
64.22.a.g 1
64.22.a.h 2
64.22.a.i 2
64.22.a.j 2
64.22.a.k 2
64.22.a.l 3
64.22.a.m 3
64.22.a.n 4
64.22.a.o 5
64.22.a.p 5
64.22.a.q 6
64.22.b \(\chi_{64}(33, \cdot)\) 64.22.b.a 2 1
64.22.b.b 12
64.22.b.c 28
64.22.e \(\chi_{64}(17, \cdot)\) 64.22.e.a 82 2
64.22.g \(\chi_{64}(9, \cdot)\) None 0 4
64.22.i \(\chi_{64}(5, \cdot)\) n/a 1336 8

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

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(64)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)