Properties

Label 663.1
Level 663
Weight 1
Dimension 14
Nonzero newspaces 3
Newform subspaces 8
Sturm bound 32256
Trace bound 4

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Defining parameters

Level: \( N \) = \( 663 = 3 \cdot 13 \cdot 17 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 8 \)
Sturm bound: \(32256\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(663))\).

Total New Old
Modular forms 784 346 438
Cusp forms 16 14 2
Eisenstein series 768 332 436

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 14 0 0 0

Trace form

\( 14q + 2q^{4} + 2q^{9} + O(q^{10}) \) \( 14q + 2q^{4} + 2q^{9} + 6q^{13} + 8q^{15} - 6q^{16} - 4q^{19} - 2q^{25} - 4q^{33} + 2q^{36} - 8q^{42} - 4q^{43} + 2q^{49} + 6q^{51} - 6q^{52} + 4q^{55} - 4q^{60} - 6q^{64} - 4q^{67} - 4q^{69} - 4q^{76} + 2q^{81} - 4q^{85} - 4q^{87} - 8q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(663))\)

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
663.1.c \(\chi_{663}(443, \cdot)\) None 0 1
663.1.d \(\chi_{663}(560, \cdot)\) None 0 1
663.1.g \(\chi_{663}(662, \cdot)\) 663.1.g.a 1 1
663.1.g.b 1
663.1.g.c 2
663.1.g.d 2
663.1.h \(\chi_{663}(545, \cdot)\) None 0 1
663.1.k \(\chi_{663}(38, \cdot)\) None 0 2
663.1.l \(\chi_{663}(268, \cdot)\) None 0 2
663.1.o \(\chi_{663}(307, \cdot)\) None 0 2
663.1.p \(\chi_{663}(424, \cdot)\) None 0 2
663.1.s \(\chi_{663}(421, \cdot)\) None 0 2
663.1.t \(\chi_{663}(404, \cdot)\) None 0 2
663.1.v \(\chi_{663}(101, \cdot)\) 663.1.v.a 2 2
663.1.v.b 2
663.1.x \(\chi_{663}(290, \cdot)\) None 0 2
663.1.y \(\chi_{663}(35, \cdot)\) None 0 2
663.1.bb \(\chi_{663}(152, \cdot)\) 663.1.bb.a 2 2
663.1.bb.b 2
663.1.bc \(\chi_{663}(151, \cdot)\) None 0 4
663.1.be \(\chi_{663}(77, \cdot)\) None 0 4
663.1.bf \(\chi_{663}(53, \cdot)\) None 0 4
663.1.bj \(\chi_{663}(70, \cdot)\) None 0 4
663.1.bl \(\chi_{663}(191, \cdot)\) None 0 4
663.1.bn \(\chi_{663}(106, \cdot)\) None 0 4
663.1.bo \(\chi_{663}(67, \cdot)\) None 0 4
663.1.br \(\chi_{663}(154, \cdot)\) None 0 4
663.1.bs \(\chi_{663}(310, \cdot)\) None 0 4
663.1.bu \(\chi_{663}(140, \cdot)\) None 0 4
663.1.bw \(\chi_{663}(44, \cdot)\) None 0 8
663.1.bz \(\chi_{663}(5, \cdot)\) None 0 8
663.1.cb \(\chi_{663}(40, \cdot)\) None 0 8
663.1.cc \(\chi_{663}(142, \cdot)\) None 0 8
663.1.ce \(\chi_{663}(19, \cdot)\) None 0 8
663.1.ci \(\chi_{663}(134, \cdot)\) None 0 8
663.1.cj \(\chi_{663}(185, \cdot)\) None 0 8
663.1.cl \(\chi_{663}(145, \cdot)\) None 0 8
663.1.cn \(\chi_{663}(10, \cdot)\) None 0 16
663.1.co \(\chi_{663}(22, \cdot)\) None 0 16
663.1.cq \(\chi_{663}(20, \cdot)\) None 0 16
663.1.ct \(\chi_{663}(11, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(663))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(663)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)