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Properties

Label 3963.1
Level 3963
Weight 1
Dimension 221
Nonzero newspaces 11
Newform subspaces 12
Sturm bound 1163360
Trace bound 7

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Defining parameters

Level: \( N \) = \( 3963 = 3 \cdot 1321 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 11 \)
Newform subspaces: \( 12 \)
Sturm bound: \(1163360\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3963))\).

Total New Old
Modular forms 2861 1539 1322
Cusp forms 221 221 0
Eisenstein series 2640 1318 1322

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 221 0 0 0

Trace form

\( 221 q - 3 q^{3} + q^{4} - 2 q^{7} + q^{9} + O(q^{10}) \) \( 221 q - 3 q^{3} + q^{4} - 2 q^{7} + q^{9} - 3 q^{12} - 2 q^{13} + q^{16} - 2 q^{19} - 2 q^{21} + q^{25} - 3 q^{27} - 2 q^{28} - 2 q^{31} + q^{36} - 2 q^{37} - 2 q^{39} - 2 q^{43} - 3 q^{48} - q^{49} - 2 q^{52} - 2 q^{57} - 2 q^{61} - 2 q^{63} + q^{64} - 2 q^{67} - 2 q^{73} - 3 q^{75} - 2 q^{76} - 2 q^{79} + q^{81} - 2 q^{84} - 4 q^{91} - 2 q^{93} - 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3963))\)

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
3963.1.b \(\chi_{3963}(3962, \cdot)\) 3963.1.b.a 1 1
3963.1.b.b 2
3963.1.c \(\chi_{3963}(1322, \cdot)\) None 0 1
3963.1.g \(\chi_{3963}(257, \cdot)\) 3963.1.g.a 2 2
3963.1.j \(\chi_{3963}(2939, \cdot)\) None 0 2
3963.1.k \(\chi_{3963}(1619, \cdot)\) None 0 2
3963.1.m \(\chi_{3963}(235, \cdot)\) None 0 4
3963.1.o \(\chi_{3963}(1385, \cdot)\) 3963.1.o.a 4 4
3963.1.p \(\chi_{3963}(1454, \cdot)\) 3963.1.p.a 4 4
3963.1.r \(\chi_{3963}(32, \cdot)\) None 0 4
3963.1.u \(\chi_{3963}(8, \cdot)\) 3963.1.u.a 8 8
3963.1.w \(\chi_{3963}(722, \cdot)\) 3963.1.w.a 10 10
3963.1.x \(\chi_{3963}(383, \cdot)\) 3963.1.x.a 10 10
3963.1.z \(\chi_{3963}(406, \cdot)\) None 0 8
3963.1.bb \(\chi_{3963}(578, \cdot)\) None 0 8
3963.1.bc \(\chi_{3963}(743, \cdot)\) None 0 8
3963.1.bf \(\chi_{3963}(34, \cdot)\) None 0 16
3963.1.bi \(\chi_{3963}(71, \cdot)\) 3963.1.bi.a 20 20
3963.1.bl \(\chi_{3963}(2, \cdot)\) None 0 16
3963.1.bn \(\chi_{3963}(704, \cdot)\) None 0 20
3963.1.bo \(\chi_{3963}(53, \cdot)\) None 0 20
3963.1.bp \(\chi_{3963}(79, \cdot)\) None 0 40
3963.1.bs \(\chi_{3963}(227, \cdot)\) 3963.1.bs.a 40 40
3963.1.bt \(\chi_{3963}(44, \cdot)\) 3963.1.bt.a 40 40
3963.1.bv \(\chi_{3963}(136, \cdot)\) None 0 32
3963.1.bw \(\chi_{3963}(62, \cdot)\) None 0 40
3963.1.bz \(\chi_{3963}(74, \cdot)\) 3963.1.bz.a 80 80
3963.1.cc \(\chi_{3963}(7, \cdot)\) None 0 80
3963.1.cd \(\chi_{3963}(98, \cdot)\) None 0 80
3963.1.ce \(\chi_{3963}(11, \cdot)\) None 0 80
3963.1.ch \(\chi_{3963}(46, \cdot)\) None 0 160
3963.1.cj \(\chi_{3963}(5, \cdot)\) None 0 160
3963.1.ck \(\chi_{3963}(13, \cdot)\) None 0 320