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Properties

Label 1539.1
Level 1539
Weight 1
Dimension 50
Nonzero newspaces 10
Newform subspaces 17
Sturm bound 174960
Trace bound 43

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Defining parameters

Level: \( N \) = \( 1539 = 3^{4} \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 17 \)
Sturm bound: \(174960\)
Trace bound: \(43\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1539))\).

Total New Old
Modular forms 2055 1002 1053
Cusp forms 111 50 61
Eisenstein series 1944 952 992

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 46 4 0 0

Trace form

\( 50 q + q^{4} + 6 q^{7} + O(q^{10}) \) \( 50 q + q^{4} + 6 q^{7} + 2 q^{13} - 3 q^{16} - 2 q^{19} + q^{25} - 4 q^{28} + 2 q^{31} - 4 q^{37} + 6 q^{43} + 3 q^{49} + 2 q^{52} - 16 q^{55} + 4 q^{58} - 2 q^{61} + 6 q^{64} + 2 q^{67} - 16 q^{73} + q^{76} + 2 q^{79} - 4 q^{82} - 8 q^{91} + 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1539))\)

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
1539.1.b \(\chi_{1539}(647, \cdot)\) None 0 1
1539.1.c \(\chi_{1539}(892, \cdot)\) 1539.1.c.a 1 1
1539.1.c.b 1
1539.1.c.c 2
1539.1.c.d 2
1539.1.c.e 2
1539.1.i \(\chi_{1539}(1243, \cdot)\) 1539.1.i.a 2 2
1539.1.j \(\chi_{1539}(26, \cdot)\) 1539.1.j.a 2 2
1539.1.n \(\chi_{1539}(539, \cdot)\) 1539.1.n.a 2 2
1539.1.o \(\chi_{1539}(379, \cdot)\) 1539.1.o.a 2 2
1539.1.o.b 2
1539.1.o.c 2
1539.1.o.d 4
1539.1.p \(\chi_{1539}(487, \cdot)\) None 0 2
1539.1.q \(\chi_{1539}(134, \cdot)\) None 0 2
1539.1.r \(\chi_{1539}(809, \cdot)\) None 0 2
1539.1.s \(\chi_{1539}(217, \cdot)\) 1539.1.s.a 2 2
1539.1.bg \(\chi_{1539}(206, \cdot)\) None 0 6
1539.1.bh \(\chi_{1539}(127, \cdot)\) None 0 6
1539.1.bl \(\chi_{1539}(359, \cdot)\) None 0 6
1539.1.bm \(\chi_{1539}(451, \cdot)\) None 0 6
1539.1.bn \(\chi_{1539}(10, \cdot)\) None 0 6
1539.1.bq \(\chi_{1539}(377, \cdot)\) 1539.1.bq.a 6 6
1539.1.br \(\chi_{1539}(325, \cdot)\) None 0 6
1539.1.bs \(\chi_{1539}(80, \cdot)\) None 0 6
1539.1.bt \(\chi_{1539}(109, \cdot)\) 1539.1.bt.a 6 6
1539.1.bx \(\chi_{1539}(316, \cdot)\) None 0 6
1539.1.by \(\chi_{1539}(368, \cdot)\) None 0 6
1539.1.bz \(\chi_{1539}(305, \cdot)\) None 0 6
1539.1.ca \(\chi_{1539}(37, \cdot)\) None 0 6
1539.1.cb \(\chi_{1539}(46, \cdot)\) None 0 6
1539.1.cc \(\chi_{1539}(125, \cdot)\) None 0 6
1539.1.ce \(\chi_{1539}(136, \cdot)\) 1539.1.ce.a 6 6
1539.1.cf \(\chi_{1539}(188, \cdot)\) 1539.1.cf.a 6 6
1539.1.ci \(\chi_{1539}(503, \cdot)\) None 0 6
1539.1.cj \(\chi_{1539}(35, \cdot)\) None 0 6
1539.1.ck \(\chi_{1539}(91, \cdot)\) None 0 6
1539.1.cl \(\chi_{1539}(307, \cdot)\) None 0 6
1539.1.cm \(\chi_{1539}(17, \cdot)\) None 0 6
1539.1.cn \(\chi_{1539}(181, \cdot)\) None 0 6
1539.1.co \(\chi_{1539}(233, \cdot)\) None 0 6
1539.1.cz \(\chi_{1539}(22, \cdot)\) None 0 18
1539.1.db \(\chi_{1539}(5, \cdot)\) None 0 18
1539.1.dc \(\chi_{1539}(101, \cdot)\) None 0 18
1539.1.de \(\chi_{1539}(158, \cdot)\) None 0 18
1539.1.df \(\chi_{1539}(13, \cdot)\) None 0 18
1539.1.dg \(\chi_{1539}(67, \cdot)\) None 0 18
1539.1.dh \(\chi_{1539}(31, \cdot)\) None 0 18
1539.1.di \(\chi_{1539}(94, \cdot)\) None 0 18
1539.1.dj \(\chi_{1539}(88, \cdot)\) None 0 18
1539.1.dm \(\chi_{1539}(20, \cdot)\) None 0 18
1539.1.dn \(\chi_{1539}(11, \cdot)\) None 0 18
1539.1.do \(\chi_{1539}(68, \cdot)\) None 0 18
1539.1.dq \(\chi_{1539}(74, \cdot)\) None 0 18
1539.1.ds \(\chi_{1539}(23, \cdot)\) None 0 18
1539.1.du \(\chi_{1539}(52, \cdot)\) None 0 18
1539.1.dv \(\chi_{1539}(205, \cdot)\) None 0 18
1539.1.dw \(\chi_{1539}(124, \cdot)\) None 0 18
1539.1.dz \(\chi_{1539}(218, \cdot)\) None 0 18

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1539))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1539)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(513))\)\(^{\oplus 2}\)