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Properties

Label 1044.1
Level 1044
Weight 1
Dimension 66
Nonzero newspaces 6
Newform subspaces 10
Sturm bound 60480
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1044 = 2^{2} \cdot 3^{2} \cdot 29 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 10 \)
Sturm bound: \(60480\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1044))\).

Total New Old
Modular forms 1234 308 926
Cusp forms 114 66 48
Eisenstein series 1120 242 878

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 66 0 0 0

Trace form

\( 66 q + q^{2} - 3 q^{4} + 4 q^{5} + q^{8} + O(q^{10}) \) \( 66 q + q^{2} - 3 q^{4} + 4 q^{5} + q^{8} - 2 q^{10} - 8 q^{13} - 7 q^{16} + 2 q^{17} - 3 q^{20} + 4 q^{22} - 13 q^{25} - 5 q^{26} + 6 q^{28} - 7 q^{29} - 6 q^{30} + q^{32} - 6 q^{33} - 11 q^{34} - 2 q^{37} + 2 q^{38} - 9 q^{40} + 2 q^{41} + 12 q^{45} - 13 q^{49} + 3 q^{50} - 6 q^{52} - 3 q^{53} + 12 q^{54} + q^{58} - 2 q^{61} + 2 q^{62} + 9 q^{64} + q^{65} + 2 q^{68} - 9 q^{73} + 2 q^{74} - 6 q^{78} + 4 q^{80} - 6 q^{82} - 4 q^{85} + 2 q^{86} - 2 q^{88} + 2 q^{89} - 6 q^{93} - 8 q^{94} - 9 q^{97} + q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1044))\)

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
1044.1.d \(\chi_{1044}(233, \cdot)\) None 0 1
1044.1.e \(\chi_{1044}(521, \cdot)\) None 0 1
1044.1.f \(\chi_{1044}(523, \cdot)\) None 0 1
1044.1.g \(\chi_{1044}(811, \cdot)\) 1044.1.g.a 1 1
1044.1.g.b 1
1044.1.g.c 2
1044.1.g.d 4
1044.1.k \(\chi_{1044}(505, \cdot)\) None 0 2
1044.1.l \(\chi_{1044}(215, \cdot)\) 1044.1.l.a 4 2
1044.1.o \(\chi_{1044}(115, \cdot)\) 1044.1.o.a 6 2
1044.1.o.b 6
1044.1.p \(\chi_{1044}(175, \cdot)\) None 0 2
1044.1.q \(\chi_{1044}(173, \cdot)\) None 0 2
1044.1.r \(\chi_{1044}(581, \cdot)\) None 0 2
1044.1.w \(\chi_{1044}(191, \cdot)\) None 0 4
1044.1.x \(\chi_{1044}(133, \cdot)\) None 0 4
1044.1.ba \(\chi_{1044}(91, \cdot)\) 1044.1.ba.a 12 6
1044.1.bb \(\chi_{1044}(199, \cdot)\) 1044.1.bb.a 6 6
1044.1.bc \(\chi_{1044}(125, \cdot)\) None 0 6
1044.1.bd \(\chi_{1044}(53, \cdot)\) None 0 6
1044.1.bi \(\chi_{1044}(143, \cdot)\) 1044.1.bi.a 24 12
1044.1.bj \(\chi_{1044}(37, \cdot)\) None 0 12
1044.1.bn \(\chi_{1044}(65, \cdot)\) None 0 12
1044.1.bo \(\chi_{1044}(5, \cdot)\) None 0 12
1044.1.bp \(\chi_{1044}(7, \cdot)\) None 0 12
1044.1.bq \(\chi_{1044}(67, \cdot)\) None 0 12
1044.1.bt \(\chi_{1044}(61, \cdot)\) None 0 24
1044.1.bu \(\chi_{1044}(11, \cdot)\) None 0 24

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1044))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1044)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(174))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(261))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(348))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(522))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1044))\)\(^{\oplus 1}\)