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Properties

Label 3456.1
Level 3456
Weight 1
Dimension 56
Nonzero newspaces 8
Newform subspaces 15
Sturm bound 663552
Trace bound 33

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Defining parameters

Level: \( N \) = \( 3456 = 2^{7} \cdot 3^{3} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 15 \)
Sturm bound: \(663552\)
Trace bound: \(33\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3456))\).

Total New Old
Modular forms 5242 824 4418
Cusp forms 442 56 386
Eisenstein series 4800 768 4032

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 40 0 16 0

Trace form

\( 56 q + O(q^{10}) \) \( 56 q + 8 q^{13} - 4 q^{17} + 4 q^{41} + 12 q^{57} + 8 q^{85} + 20 q^{89} + 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3456))\)

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
3456.1.b \(\chi_{3456}(703, \cdot)\) 3456.1.b.a 4 1
3456.1.e \(\chi_{3456}(1025, \cdot)\) 3456.1.e.a 2 1
3456.1.e.b 2
3456.1.e.c 2
3456.1.e.d 2
3456.1.g \(\chi_{3456}(2431, \cdot)\) None 0 1
3456.1.h \(\chi_{3456}(2753, \cdot)\) 3456.1.h.a 2 1
3456.1.h.b 2
3456.1.j \(\chi_{3456}(161, \cdot)\) 3456.1.j.a 4 2
3456.1.j.b 4
3456.1.m \(\chi_{3456}(1567, \cdot)\) None 0 2
3456.1.n \(\chi_{3456}(449, \cdot)\) 3456.1.n.a 2 2
3456.1.n.b 2
3456.1.o \(\chi_{3456}(127, \cdot)\) None 0 2
3456.1.q \(\chi_{3456}(2177, \cdot)\) None 0 2
3456.1.t \(\chi_{3456}(1855, \cdot)\) 3456.1.t.a 4 2
3456.1.u \(\chi_{3456}(271, \cdot)\) None 0 4
3456.1.x \(\chi_{3456}(593, \cdot)\) None 0 4
3456.1.ba \(\chi_{3456}(415, \cdot)\) None 0 4
3456.1.bb \(\chi_{3456}(737, \cdot)\) None 0 4
3456.1.bd \(\chi_{3456}(377, \cdot)\) None 0 8
3456.1.bg \(\chi_{3456}(55, \cdot)\) None 0 8
3456.1.bh \(\chi_{3456}(319, \cdot)\) 3456.1.bh.a 12 6
3456.1.bi \(\chi_{3456}(511, \cdot)\) None 0 6
3456.1.bk \(\chi_{3456}(257, \cdot)\) None 0 6
3456.1.bn \(\chi_{3456}(65, \cdot)\) 3456.1.bn.a 6 6
3456.1.bn.b 6
3456.1.bp \(\chi_{3456}(559, \cdot)\) None 0 8
3456.1.bq \(\chi_{3456}(17, \cdot)\) None 0 8
3456.1.bs \(\chi_{3456}(163, \cdot)\) None 0 16
3456.1.bv \(\chi_{3456}(53, \cdot)\) None 0 16
3456.1.bx \(\chi_{3456}(31, \cdot)\) None 0 12
3456.1.by \(\chi_{3456}(353, \cdot)\) None 0 12
3456.1.ca \(\chi_{3456}(199, \cdot)\) None 0 16
3456.1.cd \(\chi_{3456}(89, \cdot)\) None 0 16
3456.1.ce \(\chi_{3456}(113, \cdot)\) None 0 24
3456.1.ch \(\chi_{3456}(79, \cdot)\) None 0 24
3456.1.cj \(\chi_{3456}(125, \cdot)\) None 0 32
3456.1.ck \(\chi_{3456}(19, \cdot)\) None 0 32
3456.1.cn \(\chi_{3456}(41, \cdot)\) None 0 48
3456.1.co \(\chi_{3456}(7, \cdot)\) None 0 48
3456.1.cq \(\chi_{3456}(5, \cdot)\) None 0 96
3456.1.ct \(\chi_{3456}(43, \cdot)\) None 0 96

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3456))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3456)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(864))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1728))\)\(^{\oplus 2}\)