Properties

Label 228.2
Level 228
Weight 2
Dimension 594
Nonzero newspaces 12
Newform subspaces 24
Sturm bound 5760
Trace bound 1

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Defining parameters

Level: \( N \) = \( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 24 \)
Sturm bound: \(5760\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(228))\).

Total New Old
Modular forms 1620 658 962
Cusp forms 1261 594 667
Eisenstein series 359 64 295

Trace form

\( 594 q - 18 q^{4} - 9 q^{6} - 18 q^{9} - 18 q^{10} - 9 q^{12} - 12 q^{13} + 18 q^{15} - 18 q^{16} + 18 q^{17} - 18 q^{18} + 42 q^{19} + 3 q^{21} - 18 q^{22} + 18 q^{23} - 9 q^{24} - 6 q^{27} - 72 q^{28}+ \cdots + 135 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)

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
228.2.a \(\chi_{228}(1, \cdot)\) 228.2.a.a 1 1
228.2.a.b 1
228.2.a.c 2
228.2.c \(\chi_{228}(191, \cdot)\) 228.2.c.a 36 1
228.2.d \(\chi_{228}(113, \cdot)\) 228.2.d.a 2 1
228.2.d.b 4
228.2.f \(\chi_{228}(151, \cdot)\) 228.2.f.a 10 1
228.2.f.b 10
228.2.i \(\chi_{228}(49, \cdot)\) 228.2.i.a 4 2
228.2.i.b 4
228.2.k \(\chi_{228}(31, \cdot)\) 228.2.k.a 20 2
228.2.k.b 20
228.2.m \(\chi_{228}(11, \cdot)\) 228.2.m.a 72 2
228.2.p \(\chi_{228}(65, \cdot)\) 228.2.p.a 2 2
228.2.p.b 2
228.2.p.c 4
228.2.p.d 4
228.2.q \(\chi_{228}(25, \cdot)\) 228.2.q.a 6 6
228.2.q.b 12
228.2.t \(\chi_{228}(29, \cdot)\) 228.2.t.a 6 6
228.2.t.b 36
228.2.v \(\chi_{228}(23, \cdot)\) 228.2.v.a 216 6
228.2.w \(\chi_{228}(67, \cdot)\) 228.2.w.a 60 6
228.2.w.b 60

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(228))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(228)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)