↑

Properties

Label 105.10
Level 105
Weight 10
Dimension 2248
Nonzero newspaces 12
Sturm bound 7680
Trace bound 4

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(7680\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(105))\).

Total New Old
Modular forms 3552 2304 1248
Cusp forms 3360 2248 1112
Eisenstein series 192 56 136

Trace form

\( 2248 q - 136 q^{2} + 618 q^{3} - 700 q^{4} + 3084 q^{5} - 1296 q^{6} + 26648 q^{7} + 67932 q^{8} - 75150 q^{9} - 137408 q^{10} + 614480 q^{11} - 297972 q^{12} - 1415016 q^{13} - 1195128 q^{14} + 962130 q^{15}+ \cdots - 10656173820 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(105))\)

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
105.10.a \(\chi_{105}(1, \cdot)\) 105.10.a.a 4 1
105.10.a.b 4
105.10.a.c 4
105.10.a.d 4
105.10.a.e 4
105.10.a.f 4
105.10.a.g 6
105.10.a.h 6
105.10.b \(\chi_{105}(41, \cdot)\) 105.10.b.a 48 1
105.10.b.b 48
105.10.d \(\chi_{105}(64, \cdot)\) 105.10.d.a 26 1
105.10.d.b 30
105.10.g \(\chi_{105}(104, \cdot)\) n/a 140 1
105.10.i \(\chi_{105}(16, \cdot)\) 105.10.i.a 22 2
105.10.i.b 22
105.10.i.c 26
105.10.i.d 26
105.10.j \(\chi_{105}(8, \cdot)\) n/a 216 2
105.10.m \(\chi_{105}(13, \cdot)\) n/a 144 2
105.10.p \(\chi_{105}(59, \cdot)\) n/a 280 2
105.10.q \(\chi_{105}(4, \cdot)\) n/a 144 2
105.10.s \(\chi_{105}(26, \cdot)\) n/a 192 2
105.10.u \(\chi_{105}(52, \cdot)\) n/a 288 4
105.10.x \(\chi_{105}(2, \cdot)\) n/a 560 4

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(105))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(105)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)