Properties

Label 675.5
Level 675
Weight 5
Dimension 46861
Nonzero newspaces 18
Sturm bound 162000
Trace bound 4

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Defining parameters

Level: \( N \) = \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(162000\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(675))\).

Total New Old
Modular forms 65640 47517 18123
Cusp forms 63960 46861 17099
Eisenstein series 1680 656 1024

Trace form

\( 46861 q - 51 q^{2} - 78 q^{3} - 121 q^{4} - 64 q^{5} - 30 q^{6} - 11 q^{7} - 185 q^{8} - 180 q^{9} + 16 q^{10} - 431 q^{11} - 411 q^{12} + 761 q^{13} + 2227 q^{14} - 96 q^{15} - 745 q^{16} - 1857 q^{17}+ \cdots + 72723 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(675))\)

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
675.5.c \(\chi_{675}(26, \cdot)\) 675.5.c.a 1 1
675.5.c.b 1
675.5.c.c 1
675.5.c.d 2
675.5.c.e 2
675.5.c.f 2
675.5.c.g 2
675.5.c.h 2
675.5.c.i 2
675.5.c.j 4
675.5.c.k 4
675.5.c.l 4
675.5.c.m 6
675.5.c.n 6
675.5.c.o 6
675.5.c.p 6
675.5.c.q 6
675.5.c.r 10
675.5.c.s 10
675.5.c.t 12
675.5.c.u 12
675.5.d \(\chi_{675}(674, \cdot)\) 675.5.d.a 2 1
675.5.d.b 2
675.5.d.c 2
675.5.d.d 2
675.5.d.e 4
675.5.d.f 4
675.5.d.g 4
675.5.d.h 8
675.5.d.i 10
675.5.d.j 10
675.5.d.k 12
675.5.d.l 12
675.5.d.m 12
675.5.d.n 12
675.5.g \(\chi_{675}(82, \cdot)\) n/a 192 2
675.5.i \(\chi_{675}(224, \cdot)\) n/a 140 2
675.5.j \(\chi_{675}(251, \cdot)\) n/a 146 2
675.5.m \(\chi_{675}(134, \cdot)\) n/a 640 4
675.5.o \(\chi_{675}(161, \cdot)\) n/a 640 4
675.5.p \(\chi_{675}(118, \cdot)\) n/a 280 4
675.5.s \(\chi_{675}(74, \cdot)\) n/a 1284 6
675.5.t \(\chi_{675}(101, \cdot)\) n/a 1350 6
675.5.v \(\chi_{675}(28, \cdot)\) n/a 1280 8
675.5.x \(\chi_{675}(71, \cdot)\) n/a 944 8
675.5.z \(\chi_{675}(44, \cdot)\) n/a 944 8
675.5.bb \(\chi_{675}(7, \cdot)\) n/a 2568 12
675.5.be \(\chi_{675}(37, \cdot)\) n/a 1888 16
675.5.bf \(\chi_{675}(11, \cdot)\) n/a 8592 24
675.5.bh \(\chi_{675}(14, \cdot)\) n/a 8592 24
675.5.bj \(\chi_{675}(13, \cdot)\) n/a 17184 48

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(675))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(675)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)