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Properties

Label 1224.1
Level 1224
Weight 1
Dimension 83
Nonzero newspaces 9
Newform subspaces 17
Sturm bound 82944
Trace bound 11

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Defining parameters

Level: \( N \) = \( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 17 \)
Sturm bound: \(82944\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1224))\).

Total New Old
Modular forms 1788 353 1435
Cusp forms 252 83 169
Eisenstein series 1536 270 1266

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 79 0 4 0

Trace form

\( 83 q + 3 q^{2} + 2 q^{3} + 5 q^{4} + 2 q^{6} + 8 q^{7} - 3 q^{8} + 2 q^{9} + O(q^{10}) \) \( 83 q + 3 q^{2} + 2 q^{3} + 5 q^{4} + 2 q^{6} + 8 q^{7} - 3 q^{8} + 2 q^{9} - 4 q^{12} - 4 q^{13} - 3 q^{16} + 3 q^{17} - 4 q^{18} - 2 q^{19} - 4 q^{22} + 2 q^{24} + 5 q^{25} - 4 q^{27} + 3 q^{32} - 2 q^{33} - 6 q^{34} + 2 q^{36} - 24 q^{38} + 6 q^{44} + 2 q^{48} + 9 q^{49} - 21 q^{50} - q^{51} - 14 q^{54} + 4 q^{55} - 2 q^{57} - q^{64} - 12 q^{66} - 4 q^{67} - 8 q^{70} + 2 q^{72} + 2 q^{73} + 2 q^{75} - 4 q^{76} - 8 q^{79} + 2 q^{81} + 2 q^{82} - 18 q^{83} + 4 q^{85} - 4 q^{88} - 6 q^{89} - 8 q^{94} - 4 q^{96} - 4 q^{97} - 3 q^{98} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1224))\)

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
1224.1.b \(\chi_{1224}(917, \cdot)\) None 0 1
1224.1.d \(\chi_{1224}(307, \cdot)\) None 0 1
1224.1.g \(\chi_{1224}(953, \cdot)\) None 0 1
1224.1.i \(\chi_{1224}(271, \cdot)\) None 0 1
1224.1.k \(\chi_{1224}(919, \cdot)\) None 0 1
1224.1.m \(\chi_{1224}(305, \cdot)\) 1224.1.m.a 2 1
1224.1.m.b 2
1224.1.n \(\chi_{1224}(883, \cdot)\) 1224.1.n.a 1 1
1224.1.n.b 2
1224.1.n.c 2
1224.1.p \(\chi_{1224}(341, \cdot)\) None 0 1
1224.1.s \(\chi_{1224}(523, \cdot)\) 1224.1.s.a 2 2
1224.1.u \(\chi_{1224}(557, \cdot)\) None 0 2
1224.1.v \(\chi_{1224}(89, \cdot)\) None 0 2
1224.1.x \(\chi_{1224}(55, \cdot)\) None 0 2
1224.1.z \(\chi_{1224}(749, \cdot)\) None 0 2
1224.1.bb \(\chi_{1224}(67, \cdot)\) 1224.1.bb.a 2 2
1224.1.bb.b 2
1224.1.bc \(\chi_{1224}(713, \cdot)\) None 0 2
1224.1.be \(\chi_{1224}(103, \cdot)\) None 0 2
1224.1.bg \(\chi_{1224}(679, \cdot)\) None 0 2
1224.1.bi \(\chi_{1224}(137, \cdot)\) None 0 2
1224.1.bl \(\chi_{1224}(715, \cdot)\) None 0 2
1224.1.bn \(\chi_{1224}(101, \cdot)\) None 0 2
1224.1.bo \(\chi_{1224}(161, \cdot)\) None 0 4
1224.1.bp \(\chi_{1224}(127, \cdot)\) None 0 4
1224.1.bu \(\chi_{1224}(53, \cdot)\) 1224.1.bu.a 4 4
1224.1.bu.b 4
1224.1.bv \(\chi_{1224}(19, \cdot)\) 1224.1.bv.a 4 4
1224.1.bw \(\chi_{1224}(353, \cdot)\) None 0 4
1224.1.by \(\chi_{1224}(319, \cdot)\) None 0 4
1224.1.cb \(\chi_{1224}(115, \cdot)\) 1224.1.cb.a 4 4
1224.1.cb.b 4
1224.1.cd \(\chi_{1224}(149, \cdot)\) None 0 4
1224.1.ce \(\chi_{1224}(107, \cdot)\) None 0 8
1224.1.ch \(\chi_{1224}(37, \cdot)\) None 0 8
1224.1.ci \(\chi_{1224}(73, \cdot)\) None 0 8
1224.1.cl \(\chi_{1224}(71, \cdot)\) None 0 8
1224.1.co \(\chi_{1224}(77, \cdot)\) None 0 8
1224.1.cp \(\chi_{1224}(43, \cdot)\) 1224.1.cp.a 8 8
1224.1.cp.b 8
1224.1.cq \(\chi_{1224}(185, \cdot)\) None 0 8
1224.1.cr \(\chi_{1224}(151, \cdot)\) None 0 8
1224.1.cu \(\chi_{1224}(61, \cdot)\) None 0 16
1224.1.cx \(\chi_{1224}(11, \cdot)\) 1224.1.cx.a 16 16
1224.1.cx.b 16
1224.1.cy \(\chi_{1224}(23, \cdot)\) None 0 16
1224.1.db \(\chi_{1224}(97, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1224))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1224)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(408))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(612))\)\(^{\oplus 2}\)