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Properties

Label 3743.1
Level 3743
Weight 1
Dimension 123
Nonzero newspaces 5
Newform subspaces 10
Sturm bound 1164240
Trace bound 55

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Defining parameters

Level: \( N \) = \( 3743 = 19 \cdot 197 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 10 \)
Sturm bound: \(1164240\)
Trace bound: \(55\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3743))\).

Total New Old
Modular forms 3651 3437 214
Cusp forms 123 123 0
Eisenstein series 3528 3314 214

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 123 0 0 0

Trace form

\( 123 q + 25 q^{4} - 2 q^{5} - 4 q^{6} - 2 q^{7} + 25 q^{9} + O(q^{10}) \) \( 123 q + 25 q^{4} - 2 q^{5} - 4 q^{6} - 2 q^{7} + 25 q^{9} - 2 q^{11} + 21 q^{16} - 2 q^{17} - 3 q^{19} - 2 q^{20} - 2 q^{23} - 8 q^{24} + 23 q^{25} - 4 q^{26} - 10 q^{28} - 4 q^{35} + 17 q^{36} - 4 q^{39} - 8 q^{42} - 2 q^{43} - 2 q^{44} - 2 q^{45} - 6 q^{47} + 19 q^{49} - 8 q^{54} - 4 q^{55} - 6 q^{61} - 4 q^{62} - 10 q^{63} + 21 q^{64} - 2 q^{68} - 2 q^{73} - 3 q^{76} - 4 q^{77} - 2 q^{80} + 21 q^{81} - 6 q^{83} - 4 q^{85} - 10 q^{92} - 4 q^{93} - 2 q^{95} - 12 q^{96} - 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3743))\)

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
3743.1.c \(\chi_{3743}(3153, \cdot)\) None 0 1
3743.1.d \(\chi_{3743}(3742, \cdot)\) 3743.1.d.a 1 1
3743.1.d.b 2
3743.1.d.c 3
3743.1.d.d 3
3743.1.d.e 6
3743.1.d.f 12
3743.1.f \(\chi_{3743}(1787, \cdot)\) None 0 2
3743.1.h \(\chi_{3743}(787, \cdot)\) None 0 2
3743.1.i \(\chi_{3743}(198, \cdot)\) None 0 2
3743.1.n \(\chi_{3743}(577, \cdot)\) None 0 4
3743.1.o \(\chi_{3743}(949, \cdot)\) 3743.1.o.a 6 6
3743.1.p \(\chi_{3743}(892, \cdot)\) 3743.1.p.a 6 6
3743.1.r \(\chi_{3743}(393, \cdot)\) None 0 6
3743.1.s \(\chi_{3743}(395, \cdot)\) None 0 6
3743.1.w \(\chi_{3743}(20, \cdot)\) None 0 12
3743.1.y \(\chi_{3743}(408, \cdot)\) None 0 12
3743.1.ba \(\chi_{3743}(164, \cdot)\) None 0 12
3743.1.bb \(\chi_{3743}(487, \cdot)\) None 0 12
3743.1.be \(\chi_{3743}(68, \cdot)\) None 0 24
3743.1.bg \(\chi_{3743}(37, \cdot)\) 3743.1.bg.a 42 42
3743.1.bi \(\chi_{3743}(341, \cdot)\) 3743.1.bi.a 42 42
3743.1.bk \(\chi_{3743}(375, \cdot)\) None 0 36
3743.1.bl \(\chi_{3743}(33, \cdot)\) None 0 36
3743.1.bo \(\chi_{3743}(58, \cdot)\) None 0 84
3743.1.bp \(\chi_{3743}(120, \cdot)\) None 0 72
3743.1.br \(\chi_{3743}(65, \cdot)\) None 0 84
3743.1.bs \(\chi_{3743}(88, \cdot)\) None 0 84
3743.1.bv \(\chi_{3743}(11, \cdot)\) None 0 168
3743.1.bx \(\chi_{3743}(29, \cdot)\) None 0 252
3743.1.bz \(\chi_{3743}(10, \cdot)\) None 0 252
3743.1.cb \(\chi_{3743}(5, \cdot)\) None 0 504