Properties

Label 1440.1
Level 1440
Weight 1
Dimension 32
Nonzero newspaces 6
Newform subspaces 9
Sturm bound 110592
Trace bound 10

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Defining parameters

Level: \( N \) = \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 9 \)
Sturm bound: \(110592\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1440))\).

Total New Old
Modular forms 2264 302 1962
Cusp forms 216 32 184
Eisenstein series 2048 270 1778

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 32 0 0 0

Trace form

\( 32 q + 4 q^{7} + O(q^{10}) \) \( 32 q + 4 q^{7} + 8 q^{10} + 2 q^{13} + 2 q^{17} + 4 q^{19} - 4 q^{21} + 8 q^{25} - 12 q^{29} + 6 q^{37} - 8 q^{45} + 6 q^{49} - 2 q^{53} + 4 q^{55} - 2 q^{65} + 4 q^{69} + 2 q^{73} - 8 q^{76} - 16 q^{79} + 4 q^{81} - 2 q^{85} + 8 q^{94} - 6 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1440))\)

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
1440.1.c \(\chi_{1440}(449, \cdot)\) 1440.1.c.a 4 1
1440.1.e \(\chi_{1440}(991, \cdot)\) None 0 1
1440.1.g \(\chi_{1440}(271, \cdot)\) None 0 1
1440.1.i \(\chi_{1440}(1169, \cdot)\) None 0 1
1440.1.j \(\chi_{1440}(1279, \cdot)\) None 0 1
1440.1.l \(\chi_{1440}(161, \cdot)\) None 0 1
1440.1.n \(\chi_{1440}(881, \cdot)\) None 0 1
1440.1.p \(\chi_{1440}(559, \cdot)\) 1440.1.p.a 1 1
1440.1.p.b 1
1440.1.r \(\chi_{1440}(199, \cdot)\) None 0 2
1440.1.s \(\chi_{1440}(521, \cdot)\) None 0 2
1440.1.v \(\chi_{1440}(143, \cdot)\) None 0 2
1440.1.y \(\chi_{1440}(433, \cdot)\) 1440.1.y.a 4 2
1440.1.ba \(\chi_{1440}(503, \cdot)\) None 0 2
1440.1.bb \(\chi_{1440}(73, \cdot)\) None 0 2
1440.1.be \(\chi_{1440}(1223, \cdot)\) None 0 2
1440.1.bf \(\chi_{1440}(793, \cdot)\) None 0 2
1440.1.bh \(\chi_{1440}(577, \cdot)\) 1440.1.bh.a 2 2
1440.1.bh.b 2
1440.1.bh.c 2
1440.1.bk \(\chi_{1440}(287, \cdot)\) None 0 2
1440.1.bn \(\chi_{1440}(89, \cdot)\) None 0 2
1440.1.bo \(\chi_{1440}(631, \cdot)\) None 0 2
1440.1.bp \(\chi_{1440}(79, \cdot)\) None 0 2
1440.1.bq \(\chi_{1440}(401, \cdot)\) None 0 2
1440.1.bs \(\chi_{1440}(641, \cdot)\) None 0 2
1440.1.bu \(\chi_{1440}(319, \cdot)\) None 0 2
1440.1.bx \(\chi_{1440}(209, \cdot)\) None 0 2
1440.1.bz \(\chi_{1440}(751, \cdot)\) None 0 2
1440.1.cb \(\chi_{1440}(31, \cdot)\) None 0 2
1440.1.cd \(\chi_{1440}(929, \cdot)\) 1440.1.cd.a 8 2
1440.1.cf \(\chi_{1440}(37, \cdot)\) None 0 4
1440.1.cg \(\chi_{1440}(467, \cdot)\) None 0 4
1440.1.cj \(\chi_{1440}(91, \cdot)\) None 0 4
1440.1.ck \(\chi_{1440}(269, \cdot)\) None 0 4
1440.1.cm \(\chi_{1440}(19, \cdot)\) 1440.1.cm.a 8 4
1440.1.cp \(\chi_{1440}(341, \cdot)\) None 0 4
1440.1.cq \(\chi_{1440}(107, \cdot)\) None 0 4
1440.1.ct \(\chi_{1440}(397, \cdot)\) None 0 4
1440.1.cw \(\chi_{1440}(151, \cdot)\) None 0 4
1440.1.cx \(\chi_{1440}(329, \cdot)\) None 0 4
1440.1.cz \(\chi_{1440}(97, \cdot)\) None 0 4
1440.1.da \(\chi_{1440}(383, \cdot)\) None 0 4
1440.1.dd \(\chi_{1440}(313, \cdot)\) None 0 4
1440.1.de \(\chi_{1440}(263, \cdot)\) None 0 4
1440.1.dh \(\chi_{1440}(553, \cdot)\) None 0 4
1440.1.di \(\chi_{1440}(23, \cdot)\) None 0 4
1440.1.dl \(\chi_{1440}(47, \cdot)\) None 0 4
1440.1.dm \(\chi_{1440}(337, \cdot)\) None 0 4
1440.1.do \(\chi_{1440}(41, \cdot)\) None 0 4
1440.1.dp \(\chi_{1440}(439, \cdot)\) None 0 4
1440.1.ds \(\chi_{1440}(133, \cdot)\) None 0 8
1440.1.dv \(\chi_{1440}(83, \cdot)\) None 0 8
1440.1.dx \(\chi_{1440}(29, \cdot)\) None 0 8
1440.1.dy \(\chi_{1440}(211, \cdot)\) None 0 8
1440.1.ea \(\chi_{1440}(101, \cdot)\) None 0 8
1440.1.ed \(\chi_{1440}(139, \cdot)\) None 0 8
1440.1.ef \(\chi_{1440}(203, \cdot)\) None 0 8
1440.1.eg \(\chi_{1440}(13, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1440))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1440)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(720))\)\(^{\oplus 2}\)