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Properties

Label 264.1
Level 264
Weight 1
Dimension 18
Nonzero newspaces 3
Newform subspaces 6
Sturm bound 3840
Trace bound 3

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Defining parameters

Level: \( N \) = \( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 6 \)
Sturm bound: \(3840\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(264))\).

Total New Old
Modular forms 270 54 216
Cusp forms 30 18 12
Eisenstein series 240 36 204

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 18 0 0 0

Trace form

\( 18 q - 2 q^{4} - 7 q^{6} - 4 q^{7} - 2 q^{9} + O(q^{10}) \) \( 18 q - 2 q^{4} - 7 q^{6} - 4 q^{7} - 2 q^{9} - 4 q^{10} + 6 q^{15} - 2 q^{16} - 5 q^{18} - 10 q^{19} - 2 q^{22} + 3 q^{24} - 6 q^{25} + 6 q^{28} + 6 q^{31} - 7 q^{33} + 3 q^{36} + 6 q^{40} + 6 q^{42} - 6 q^{49} + 5 q^{51} + 8 q^{54} - 4 q^{55} - 5 q^{57} + 6 q^{58} - 4 q^{60} - 4 q^{63} - 2 q^{64} + 2 q^{70} + 6 q^{73} + 5 q^{75} - 4 q^{79} - 2 q^{81} + 10 q^{82} - 4 q^{87} - 2 q^{88} - 4 q^{90} - 2 q^{96} - 14 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(264))\)

We only show spaces with odd 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
264.1.c \(\chi_{264}(67, \cdot)\) None 0 1
264.1.e \(\chi_{264}(109, \cdot)\) None 0 1
264.1.g \(\chi_{264}(263, \cdot)\) None 0 1
264.1.i \(\chi_{264}(89, \cdot)\) None 0 1
264.1.j \(\chi_{264}(241, \cdot)\) None 0 1
264.1.l \(\chi_{264}(199, \cdot)\) None 0 1
264.1.n \(\chi_{264}(221, \cdot)\) None 0 1
264.1.p \(\chi_{264}(131, \cdot)\) 264.1.p.a 1 1
264.1.p.b 1
264.1.r \(\chi_{264}(35, \cdot)\) 264.1.r.a 4 4
264.1.r.b 4
264.1.t \(\chi_{264}(5, \cdot)\) 264.1.t.a 4 4
264.1.t.b 4
264.1.v \(\chi_{264}(31, \cdot)\) None 0 4
264.1.x \(\chi_{264}(73, \cdot)\) None 0 4
264.1.y \(\chi_{264}(113, \cdot)\) None 0 4
264.1.ba \(\chi_{264}(95, \cdot)\) None 0 4
264.1.bc \(\chi_{264}(13, \cdot)\) None 0 4
264.1.be \(\chi_{264}(91, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(264))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(264)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 2}\)