Properties

Label 105.2
Level 105
Weight 2
Dimension 227
Nonzero newspaces 12
Newform subspaces 25
Sturm bound 1536
Trace bound 4

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Defining parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 25 \)
Sturm bound: \(1536\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(105))\).

Total New Old
Modular forms 480 283 197
Cusp forms 289 227 62
Eisenstein series 191 56 135

Trace form

\( 227 q + 5 q^{2} - 5 q^{3} - 19 q^{4} - 7 q^{5} - 35 q^{6} - 21 q^{7} - 27 q^{8} - 21 q^{9} - 43 q^{10} - 16 q^{11} - 27 q^{12} - 34 q^{13} - 27 q^{14} - 21 q^{15} - 75 q^{16} - 10 q^{17} - 7 q^{18} - 40 q^{19}+ \cdots - 124 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)

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
105.2.a \(\chi_{105}(1, \cdot)\) 105.2.a.a 1 1
105.2.a.b 2
105.2.b \(\chi_{105}(41, \cdot)\) 105.2.b.a 2 1
105.2.b.b 2
105.2.b.c 4
105.2.b.d 4
105.2.d \(\chi_{105}(64, \cdot)\) 105.2.d.a 2 1
105.2.d.b 6
105.2.g \(\chi_{105}(104, \cdot)\) 105.2.g.a 4 1
105.2.g.b 4
105.2.g.c 4
105.2.i \(\chi_{105}(16, \cdot)\) 105.2.i.a 2 2
105.2.i.b 2
105.2.i.c 4
105.2.i.d 4
105.2.j \(\chi_{105}(8, \cdot)\) 105.2.j.a 24 2
105.2.m \(\chi_{105}(13, \cdot)\) 105.2.m.a 16 2
105.2.p \(\chi_{105}(59, \cdot)\) 105.2.p.a 24 2
105.2.q \(\chi_{105}(4, \cdot)\) 105.2.q.a 16 2
105.2.s \(\chi_{105}(26, \cdot)\) 105.2.s.a 2 2
105.2.s.b 2
105.2.s.c 8
105.2.s.d 8
105.2.u \(\chi_{105}(52, \cdot)\) 105.2.u.a 32 4
105.2.x \(\chi_{105}(2, \cdot)\) 105.2.x.a 48 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(105))\) into lower level spaces

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