Properties

Label 245.6
Level 245
Weight 6
Dimension 10199
Nonzero newspaces 12
Sturm bound 28224
Trace bound 2

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Defining parameters

Level: \( N \) = \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(28224\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(245))\).

Total New Old
Modular forms 12000 10489 1511
Cusp forms 11520 10199 1321
Eisenstein series 480 290 190

Trace form

\( 10199 q - 28 q^{2} - 70 q^{3} + 174 q^{4} - 176 q^{5} - 710 q^{6} - 268 q^{7} - 858 q^{8} + 3013 q^{9} + 2655 q^{10} + 1094 q^{11} - 9146 q^{12} - 9084 q^{13} - 3516 q^{14} + 2975 q^{15} + 12454 q^{16}+ \cdots + 2785820 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(245))\)

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
245.6.a \(\chi_{245}(1, \cdot)\) 245.6.a.a 1 1
245.6.a.b 1
245.6.a.c 2
245.6.a.d 3
245.6.a.e 4
245.6.a.f 5
245.6.a.g 5
245.6.a.h 6
245.6.a.i 6
245.6.a.j 8
245.6.a.k 8
245.6.a.l 10
245.6.a.m 10
245.6.b \(\chi_{245}(99, \cdot)\) 245.6.b.a 2 1
245.6.b.b 2
245.6.b.c 12
245.6.b.d 14
245.6.b.e 18
245.6.b.f 18
245.6.b.g 32
245.6.e \(\chi_{245}(116, \cdot)\) n/a 132 2
245.6.f \(\chi_{245}(48, \cdot)\) n/a 192 2
245.6.j \(\chi_{245}(79, \cdot)\) n/a 192 2
245.6.k \(\chi_{245}(36, \cdot)\) n/a 552 6
245.6.l \(\chi_{245}(68, \cdot)\) n/a 384 4
245.6.p \(\chi_{245}(29, \cdot)\) n/a 828 6
245.6.q \(\chi_{245}(11, \cdot)\) n/a 1128 12
245.6.s \(\chi_{245}(13, \cdot)\) n/a 1656 12
245.6.t \(\chi_{245}(4, \cdot)\) n/a 1656 12
245.6.x \(\chi_{245}(3, \cdot)\) n/a 3312 24

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(245))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(245)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)