Properties

Label 121.4
Level 121
Weight 4
Dimension 1715
Nonzero newspaces 4
Newform subspaces 20
Sturm bound 4840
Trace bound 1

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Defining parameters

Level: \( N \) = \( 121 = 11^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 20 \)
Sturm bound: \(4840\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(121))\).

Total New Old
Modular forms 1895 1856 39
Cusp forms 1735 1715 20
Eisenstein series 160 141 19

Trace form

\( 1715 q - 45 q^{2} - 45 q^{3} - 45 q^{4} - 45 q^{5} + 55 q^{6} - 25 q^{7} - 125 q^{8} - 205 q^{9} - 235 q^{10} - 100 q^{11} - 405 q^{12} - 85 q^{13} + 345 q^{14} + 575 q^{15} + 715 q^{16} + 255 q^{17} - 35 q^{18}+ \cdots - 1670 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(121))\)

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
121.4.a \(\chi_{121}(1, \cdot)\) 121.4.a.a 1 1
121.4.a.b 2
121.4.a.c 2
121.4.a.d 2
121.4.a.e 2
121.4.a.f 4
121.4.a.g 4
121.4.a.h 6
121.4.c \(\chi_{121}(3, \cdot)\) 121.4.c.a 4 4
121.4.c.b 8
121.4.c.c 8
121.4.c.d 8
121.4.c.e 8
121.4.c.f 8
121.4.c.g 8
121.4.c.h 8
121.4.c.i 8
121.4.c.j 24
121.4.e \(\chi_{121}(12, \cdot)\) 121.4.e.a 320 10
121.4.g \(\chi_{121}(4, \cdot)\) 121.4.g.a 1280 40

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(121))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(121)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)