Properties

Label 1444.1
Level 1444
Weight 1
Dimension 62
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 129960
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1444 = 2^{2} \cdot 19^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(129960\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1444))\).

Total New Old
Modular forms 1324 531 793
Cusp forms 64 62 2
Eisenstein series 1260 469 791

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 44 0 18 0

Trace form

\( 62q + q^{5} + q^{7} - q^{9} + O(q^{10}) \) \( 62q + q^{5} + q^{7} - q^{9} + q^{11} + q^{17} - 18q^{20} - 2q^{23} - q^{35} + q^{43} + q^{45} + q^{47} - q^{55} - 18q^{58} + q^{61} + q^{63} + q^{73} - 10q^{77} - q^{81} - 2q^{83} - q^{85} + q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1444))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1444.1.b \(\chi_{1444}(723, \cdot)\) 1444.1.b.a 2 1
1444.1.b.b 2
1444.1.c \(\chi_{1444}(721, \cdot)\) 1444.1.c.a 2 1
1444.1.g \(\chi_{1444}(1151, \cdot)\) 1444.1.g.a 4 2
1444.1.g.b 4
1444.1.h \(\chi_{1444}(69, \cdot)\) 1444.1.h.a 2 2
1444.1.h.b 4
1444.1.j \(\chi_{1444}(333, \cdot)\) 1444.1.j.a 6 6
1444.1.j.b 12
1444.1.l \(\chi_{1444}(99, \cdot)\) 1444.1.l.a 12 6
1444.1.l.b 12
1444.1.o \(\chi_{1444}(37, \cdot)\) None 0 18
1444.1.p \(\chi_{1444}(39, \cdot)\) None 0 18
1444.1.r \(\chi_{1444}(65, \cdot)\) None 0 36
1444.1.s \(\chi_{1444}(7, \cdot)\) None 0 36
1444.1.v \(\chi_{1444}(23, \cdot)\) None 0 108
1444.1.x \(\chi_{1444}(13, \cdot)\) None 0 108

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1444))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1444)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)