Properties

Label 315.8
Level 315
Weight 8
Dimension 16692
Nonzero newspaces 30
Sturm bound 55296
Trace bound 9

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(55296\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(315))\).

Total New Old
Modular forms 24576 16964 7612
Cusp forms 23808 16692 7116
Eisenstein series 768 272 496

Trace form

\( 16692 q - 82 q^{2} + 88 q^{3} + 330 q^{4} - 1206 q^{5} - 4972 q^{6} + 1810 q^{7} + 25986 q^{8} + 12584 q^{9} - 8590 q^{10} - 61972 q^{11} + 4040 q^{12} - 10224 q^{13} + 138138 q^{14} + 58444 q^{15} - 116082 q^{16}+ \cdots + 76039336 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(315))\)

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
315.8.a \(\chi_{315}(1, \cdot)\) 315.8.a.a 1 1
315.8.a.b 1
315.8.a.c 2
315.8.a.d 2
315.8.a.e 3
315.8.a.f 4
315.8.a.g 4
315.8.a.h 4
315.8.a.i 4
315.8.a.j 4
315.8.a.k 4
315.8.a.l 4
315.8.a.m 5
315.8.a.n 6
315.8.a.o 6
315.8.a.p 8
315.8.a.q 8
315.8.b \(\chi_{315}(251, \cdot)\) 315.8.b.a 36 1
315.8.b.b 36
315.8.d \(\chi_{315}(64, \cdot)\) n/a 106 1
315.8.g \(\chi_{315}(314, \cdot)\) n/a 112 1
315.8.i \(\chi_{315}(106, \cdot)\) n/a 336 2
315.8.j \(\chi_{315}(46, \cdot)\) n/a 188 2
315.8.k \(\chi_{315}(16, \cdot)\) n/a 448 2
315.8.l \(\chi_{315}(121, \cdot)\) n/a 448 2
315.8.m \(\chi_{315}(8, \cdot)\) n/a 168 2
315.8.p \(\chi_{315}(118, \cdot)\) n/a 276 2
315.8.r \(\chi_{315}(184, \cdot)\) n/a 664 2
315.8.t \(\chi_{315}(101, \cdot)\) n/a 448 2
315.8.u \(\chi_{315}(59, \cdot)\) n/a 664 2
315.8.z \(\chi_{315}(104, \cdot)\) n/a 664 2
315.8.bb \(\chi_{315}(89, \cdot)\) n/a 224 2
315.8.be \(\chi_{315}(236, \cdot)\) n/a 448 2
315.8.bf \(\chi_{315}(109, \cdot)\) n/a 276 2
315.8.bh \(\chi_{315}(169, \cdot)\) n/a 504 2
315.8.bj \(\chi_{315}(26, \cdot)\) n/a 152 2
315.8.bl \(\chi_{315}(41, \cdot)\) n/a 448 2
315.8.bo \(\chi_{315}(4, \cdot)\) n/a 664 2
315.8.bq \(\chi_{315}(164, \cdot)\) n/a 664 2
315.8.bs \(\chi_{315}(52, \cdot)\) n/a 1328 4
315.8.bv \(\chi_{315}(23, \cdot)\) n/a 1328 4
315.8.bx \(\chi_{315}(2, \cdot)\) n/a 1328 4
315.8.bz \(\chi_{315}(73, \cdot)\) n/a 552 4
315.8.cb \(\chi_{315}(13, \cdot)\) n/a 1328 4
315.8.cc \(\chi_{315}(92, \cdot)\) n/a 1008 4
315.8.ce \(\chi_{315}(53, \cdot)\) n/a 448 4
315.8.cg \(\chi_{315}(157, \cdot)\) n/a 1328 4

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(315))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(315)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 2}\)