Properties

Label 49.10
Level 49
Weight 10
Dimension 822
Nonzero newspaces 4
Newform subspaces 17
Sturm bound 1960
Trace bound 1

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Defining parameters

Level: \( N \) = \( 49 = 7^{2} \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 17 \)
Sturm bound: \(1960\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(49))\).

Total New Old
Modular forms 912 871 41
Cusp forms 852 822 30
Eisenstein series 60 49 11

Trace form

\( 822 q - 15 q^{2} - 339 q^{3} - 15 q^{4} - 1719 q^{5} + 15543 q^{6} - 1386 q^{7} - 101925 q^{8} + 101373 q^{9} + 100335 q^{10} - 148191 q^{11} - 162729 q^{12} + 731955 q^{13} - 25326 q^{14} - 89163 q^{15}+ \cdots - 5220694956 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(49))\)

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
49.10.a \(\chi_{49}(1, \cdot)\) 49.10.a.a 1 1
49.10.a.b 2
49.10.a.c 3
49.10.a.d 4
49.10.a.e 5
49.10.a.f 5
49.10.a.g 8
49.10.c \(\chi_{49}(18, \cdot)\) 49.10.c.a 2 2
49.10.c.b 4
49.10.c.c 4
49.10.c.d 6
49.10.c.e 6
49.10.c.f 8
49.10.c.g 10
49.10.c.h 16
49.10.e \(\chi_{49}(8, \cdot)\) 49.10.e.a 246 6
49.10.g \(\chi_{49}(2, \cdot)\) 49.10.g.a 492 12

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(49))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(49)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)