↑

Properties

Label 273.4
Level 273
Weight 4
Dimension 5616
Nonzero newspaces 30
Sturm bound 21504
Trace bound 7

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(21504\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(273))\).

Total New Old
Modular forms 8352 5832 2520
Cusp forms 7776 5616 2160
Eisenstein series 576 216 360

Trace form

\( 5616 q - 30 q^{3} - 36 q^{4} + 48 q^{5} + 48 q^{6} - 24 q^{7} - 396 q^{8} - 102 q^{9} + 216 q^{10} + 240 q^{11} + 636 q^{12} + 612 q^{13} + 864 q^{14} + 480 q^{15} + 204 q^{16} - 732 q^{17} - 1896 q^{18}+ \cdots + 31608 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(273))\)

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
273.4.a \(\chi_{273}(1, \cdot)\) 273.4.a.a 1 1
273.4.a.b 1
273.4.a.c 1
273.4.a.d 2
273.4.a.e 4
273.4.a.f 4
273.4.a.g 5
273.4.a.h 6
273.4.a.i 6
273.4.a.j 6
273.4.c \(\chi_{273}(64, \cdot)\) 273.4.c.a 20 1
273.4.c.b 20
273.4.e \(\chi_{273}(209, \cdot)\) 273.4.e.a 96 1
273.4.g \(\chi_{273}(272, \cdot)\) n/a 108 1
273.4.i \(\chi_{273}(79, \cdot)\) 273.4.i.a 2 2
273.4.i.b 6
273.4.i.c 14
273.4.i.d 22
273.4.i.e 26
273.4.i.f 26
273.4.j \(\chi_{273}(100, \cdot)\) n/a 112 2
273.4.k \(\chi_{273}(22, \cdot)\) 273.4.k.a 2 2
273.4.k.b 2
273.4.k.c 20
273.4.k.d 20
273.4.k.e 22
273.4.k.f 22
273.4.l \(\chi_{273}(16, \cdot)\) n/a 112 2
273.4.n \(\chi_{273}(8, \cdot)\) n/a 168 2
273.4.p \(\chi_{273}(34, \cdot)\) n/a 112 2
273.4.r \(\chi_{273}(68, \cdot)\) n/a 216 2
273.4.t \(\chi_{273}(4, \cdot)\) n/a 112 2
273.4.u \(\chi_{273}(62, \cdot)\) n/a 216 2
273.4.y \(\chi_{273}(101, \cdot)\) n/a 216 2
273.4.ba \(\chi_{273}(38, \cdot)\) n/a 216 2
273.4.bd \(\chi_{273}(43, \cdot)\) 273.4.bd.a 40 2
273.4.bd.b 40
273.4.bf \(\chi_{273}(152, \cdot)\) n/a 216 2
273.4.bh \(\chi_{273}(131, \cdot)\) n/a 192 2
273.4.bj \(\chi_{273}(25, \cdot)\) n/a 112 2
273.4.bl \(\chi_{273}(88, \cdot)\) n/a 112 2
273.4.bn \(\chi_{273}(146, \cdot)\) n/a 216 2
273.4.br \(\chi_{273}(17, \cdot)\) n/a 216 2
273.4.bt \(\chi_{273}(136, \cdot)\) n/a 224 4
273.4.bv \(\chi_{273}(2, \cdot)\) n/a 432 4
273.4.bw \(\chi_{273}(11, \cdot)\) n/a 432 4
273.4.by \(\chi_{273}(76, \cdot)\) n/a 224 4
273.4.bz \(\chi_{273}(31, \cdot)\) n/a 224 4
273.4.cc \(\chi_{273}(50, \cdot)\) n/a 336 4
273.4.cd \(\chi_{273}(44, \cdot)\) n/a 432 4
273.4.cg \(\chi_{273}(19, \cdot)\) n/a 224 4

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(273))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(273)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 2}\)