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Properties

Label 1944.1
Level 1944
Weight 1
Dimension 132
Nonzero newspaces 7
Newform subspaces 14
Sturm bound 209952
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1944 = 2^{3} \cdot 3^{5} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 14 \)
Sturm bound: \(209952\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1944))\).

Total New Old
Modular forms 2560 516 2044
Cusp forms 292 132 160
Eisenstein series 2268 384 1884

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 114 0 18 0

Trace form

\( 132 q + O(q^{10}) \) \( 132 q - 12 q^{10} - 6 q^{19} + 6 q^{22} + 6 q^{34} + 9 q^{38} + 6 q^{43} - 12 q^{46} - 30 q^{55} + 9 q^{59} + 6 q^{64} + 6 q^{67} - 45 q^{68} + 6 q^{73} - 21 q^{76} + 12 q^{82} - 21 q^{88} + 9 q^{89} - 27 q^{96} + 6 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1944))\)

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
1944.1.b \(\chi_{1944}(1459, \cdot)\) None 0 1
1944.1.e \(\chi_{1944}(1457, \cdot)\) 1944.1.e.a 2 1
1944.1.g \(\chi_{1944}(487, \cdot)\) None 0 1
1944.1.h \(\chi_{1944}(485, \cdot)\) 1944.1.h.a 3 1
1944.1.h.b 3
1944.1.h.c 4
1944.1.j \(\chi_{1944}(1133, \cdot)\) 1944.1.j.a 6 2
1944.1.j.b 6
1944.1.j.c 8
1944.1.k \(\chi_{1944}(1135, \cdot)\) None 0 2
1944.1.m \(\chi_{1944}(161, \cdot)\) 1944.1.m.a 4 2
1944.1.p \(\chi_{1944}(163, \cdot)\) None 0 2
1944.1.r \(\chi_{1944}(379, \cdot)\) 1944.1.r.a 6 6
1944.1.r.b 6
1944.1.r.c 6
1944.1.r.d 6
1944.1.s \(\chi_{1944}(55, \cdot)\) None 0 6
1944.1.u \(\chi_{1944}(377, \cdot)\) None 0 6
1944.1.x \(\chi_{1944}(53, \cdot)\) None 0 6
1944.1.z \(\chi_{1944}(125, \cdot)\) None 0 18
1944.1.ba \(\chi_{1944}(127, \cdot)\) None 0 18
1944.1.bc \(\chi_{1944}(17, \cdot)\) None 0 18
1944.1.bf \(\chi_{1944}(19, \cdot)\) 1944.1.bf.a 18 18
1944.1.bh \(\chi_{1944}(43, \cdot)\) 1944.1.bh.a 54 54
1944.1.bi \(\chi_{1944}(7, \cdot)\) None 0 54
1944.1.bk \(\chi_{1944}(41, \cdot)\) None 0 54
1944.1.bn \(\chi_{1944}(5, \cdot)\) None 0 54

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1944))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1944)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(648))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(972))\)\(^{\oplus 2}\)