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Properties

Label 2592.1
Level 2592
Weight 1
Dimension 50
Nonzero newspaces 7
Newform subspaces 11
Sturm bound 373248
Trace bound 13

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Defining parameters

Level: \( N \) = \( 2592 = 2^{5} \cdot 3^{4} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 11 \)
Sturm bound: \(373248\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2592))\).

Total New Old
Modular forms 3844 610 3234
Cusp forms 388 50 338
Eisenstein series 3456 560 2896

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

\( 50 q - 2 q^{7} + O(q^{10}) \) \( 50 q - 2 q^{7} - 3 q^{11} + 4 q^{13} + 2 q^{19} + 4 q^{25} - 2 q^{31} + 4 q^{37} + 3 q^{41} + 5 q^{43} + 4 q^{49} + 9 q^{51} - 4 q^{55} + 15 q^{59} + 5 q^{67} - 6 q^{73} + 4 q^{79} - 4 q^{85} - 12 q^{89} + q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2592))\)

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
2592.1.b \(\chi_{2592}(1135, \cdot)\) 2592.1.b.a 1 1
2592.1.b.b 1
2592.1.e \(\chi_{2592}(161, \cdot)\) 2592.1.e.a 4 1
2592.1.g \(\chi_{2592}(2431, \cdot)\) 2592.1.g.a 2 1
2592.1.g.b 2
2592.1.h \(\chi_{2592}(1457, \cdot)\) None 0 1
2592.1.j \(\chi_{2592}(809, \cdot)\) None 0 2
2592.1.m \(\chi_{2592}(487, \cdot)\) None 0 2
2592.1.n \(\chi_{2592}(593, \cdot)\) 2592.1.n.a 2 2
2592.1.n.b 2
2592.1.o \(\chi_{2592}(703, \cdot)\) None 0 2
2592.1.q \(\chi_{2592}(1025, \cdot)\) 2592.1.q.a 4 2
2592.1.q.b 8
2592.1.t \(\chi_{2592}(271, \cdot)\) None 0 2
2592.1.u \(\chi_{2592}(163, \cdot)\) None 0 4
2592.1.x \(\chi_{2592}(485, \cdot)\) None 0 4
2592.1.ba \(\chi_{2592}(55, \cdot)\) None 0 4
2592.1.bb \(\chi_{2592}(377, \cdot)\) None 0 4
2592.1.bd \(\chi_{2592}(559, \cdot)\) 2592.1.bd.a 6 6
2592.1.be \(\chi_{2592}(127, \cdot)\) None 0 6
2592.1.bg \(\chi_{2592}(449, \cdot)\) None 0 6
2592.1.bj \(\chi_{2592}(17, \cdot)\) None 0 6
2592.1.bl \(\chi_{2592}(379, \cdot)\) None 0 8
2592.1.bm \(\chi_{2592}(53, \cdot)\) None 0 8
2592.1.bq \(\chi_{2592}(199, \cdot)\) None 0 12
2592.1.br \(\chi_{2592}(89, \cdot)\) None 0 12
2592.1.bt \(\chi_{2592}(113, \cdot)\) None 0 18
2592.1.bu \(\chi_{2592}(31, \cdot)\) None 0 18
2592.1.bw \(\chi_{2592}(65, \cdot)\) None 0 18
2592.1.bz \(\chi_{2592}(79, \cdot)\) 2592.1.bz.a 18 18
2592.1.ca \(\chi_{2592}(125, \cdot)\) None 0 24
2592.1.cd \(\chi_{2592}(19, \cdot)\) None 0 24
2592.1.cf \(\chi_{2592}(7, \cdot)\) None 0 36
2592.1.cg \(\chi_{2592}(41, \cdot)\) None 0 36
2592.1.cj \(\chi_{2592}(5, \cdot)\) None 0 72
2592.1.ck \(\chi_{2592}(43, \cdot)\) None 0 72

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2592))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2592)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(648))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(864))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1296))\)\(^{\oplus 2}\)