Properties

Label 242.2
Level 242
Weight 2
Dimension 596
Nonzero newspaces 4
Newform subspaces 17
Sturm bound 7260
Trace bound 1

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Defining parameters

Level: \( N \) = \( 242 = 2 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 17 \)
Sturm bound: \(7260\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(242))\).

Total New Old
Modular forms 1975 596 1379
Cusp forms 1656 596 1060
Eisenstein series 319 0 319

Trace form

\( 596 q + q^{2} + 4 q^{3} + q^{4} + 6 q^{5} - 6 q^{6} - 12 q^{7} + q^{8} - 27 q^{9} - 14 q^{10} - 10 q^{11} - 16 q^{12} - 6 q^{13} - 12 q^{14} - 36 q^{15} + q^{16} - 22 q^{17} + 3 q^{18} - 10 q^{19} + 6 q^{20}+ \cdots - 130 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)

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
242.2.a \(\chi_{242}(1, \cdot)\) 242.2.a.a 1 1
242.2.a.b 1
242.2.a.c 2
242.2.a.d 2
242.2.a.e 2
242.2.a.f 2
242.2.c \(\chi_{242}(3, \cdot)\) 242.2.c.a 4 4
242.2.c.b 4
242.2.c.c 4
242.2.c.d 4
242.2.c.e 4
242.2.c.f 8
242.2.c.g 8
242.2.e \(\chi_{242}(23, \cdot)\) 242.2.e.a 50 10
242.2.e.b 60
242.2.g \(\chi_{242}(5, \cdot)\) 242.2.g.a 200 40
242.2.g.b 240

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(242))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(242)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)