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Properties

Label 704.5
Level 704
Weight 5
Dimension 33786
Nonzero newspaces 16
Sturm bound 153600
Trace bound 9

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Defining parameters

Level: \( N \) = \( 704 = 2^{6} \cdot 11 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(153600\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(704))\).

Total New Old
Modular forms 62160 34182 27978
Cusp forms 60720 33786 26934
Eisenstein series 1440 396 1044

Trace form

\( 33786 q - 64 q^{2} - 48 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 52 q^{7} - 64 q^{8} - 242 q^{9} - 64 q^{10} + 42 q^{11} - 144 q^{12} + 640 q^{13} - 64 q^{14} - 44 q^{15} - 64 q^{16} - 1072 q^{17} - 64 q^{18}+ \cdots + 48514 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(704))\)

We only show spaces with odd 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
704.5.b \(\chi_{704}(417, \cdot)\) 704.5.b.a 4 1
704.5.b.b 4
704.5.b.c 8
704.5.b.d 24
704.5.b.e 56
704.5.d \(\chi_{704}(639, \cdot)\) 704.5.d.a 2 1
704.5.d.b 6
704.5.d.c 12
704.5.d.d 20
704.5.d.e 20
704.5.d.f 20
704.5.f \(\chi_{704}(287, \cdot)\) 704.5.f.a 24 1
704.5.f.b 56
704.5.h \(\chi_{704}(65, \cdot)\) 704.5.h.a 1 1
704.5.h.b 1
704.5.h.c 2
704.5.h.d 2
704.5.h.e 2
704.5.h.f 2
704.5.h.g 2
704.5.h.h 2
704.5.h.i 4
704.5.h.j 4
704.5.h.k 12
704.5.h.l 12
704.5.h.m 24
704.5.h.n 24
704.5.k \(\chi_{704}(111, \cdot)\) n/a 160 2
704.5.l \(\chi_{704}(241, \cdot)\) n/a 188 2
704.5.o \(\chi_{704}(153, \cdot)\) None 0 4
704.5.p \(\chi_{704}(23, \cdot)\) None 0 4
704.5.r \(\chi_{704}(129, \cdot)\) n/a 376 4
704.5.t \(\chi_{704}(31, \cdot)\) n/a 384 4
704.5.v \(\chi_{704}(191, \cdot)\) n/a 376 4
704.5.x \(\chi_{704}(161, \cdot)\) n/a 384 4
704.5.y \(\chi_{704}(21, \cdot)\) n/a 3056 8
704.5.ba \(\chi_{704}(67, \cdot)\) n/a 2560 8
704.5.bc \(\chi_{704}(17, \cdot)\) n/a 752 8
704.5.bd \(\chi_{704}(15, \cdot)\) n/a 752 8
704.5.bh \(\chi_{704}(71, \cdot)\) None 0 16
704.5.bi \(\chi_{704}(41, \cdot)\) None 0 16
704.5.bl \(\chi_{704}(3, \cdot)\) n/a 12224 32
704.5.bn \(\chi_{704}(13, \cdot)\) n/a 12224 32

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(704))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(704)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 7}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(704))\)\(^{\oplus 1}\)