Properties

Label 720.1
Level 720
Weight 1
Dimension 13
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 27648
Trace bound 10

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Defining parameters

Level: \( N \) = \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(27648\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(720))\).

Total New Old
Modular forms 980 135 845
Cusp forms 84 13 71
Eisenstein series 896 122 774

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 13 0 0 0

Trace form

\( 13 q + 3 q^{5} + 2 q^{9} + O(q^{10}) \) \( 13 q + 3 q^{5} + 2 q^{9} - 4 q^{10} + 4 q^{13} - 4 q^{16} + 4 q^{19} - q^{25} - 4 q^{34} - 4 q^{37} + 4 q^{45} + 4 q^{46} - q^{49} - 8 q^{61} - 6 q^{69} - 4 q^{73} - 4 q^{76} - 2 q^{81} - 12 q^{85} - 6 q^{89} + 4 q^{94} - 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(720))\)

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
720.1.c \(\chi_{720}(449, \cdot)\) None 0 1
720.1.e \(\chi_{720}(271, \cdot)\) None 0 1
720.1.g \(\chi_{720}(631, \cdot)\) None 0 1
720.1.i \(\chi_{720}(89, \cdot)\) None 0 1
720.1.j \(\chi_{720}(559, \cdot)\) 720.1.j.a 1 1
720.1.l \(\chi_{720}(161, \cdot)\) None 0 1
720.1.n \(\chi_{720}(521, \cdot)\) None 0 1
720.1.p \(\chi_{720}(199, \cdot)\) None 0 1
720.1.r \(\chi_{720}(19, \cdot)\) 720.1.r.a 4 2
720.1.s \(\chi_{720}(341, \cdot)\) None 0 2
720.1.v \(\chi_{720}(503, \cdot)\) None 0 2
720.1.y \(\chi_{720}(73, \cdot)\) None 0 2
720.1.ba \(\chi_{720}(107, \cdot)\) None 0 2
720.1.bb \(\chi_{720}(37, \cdot)\) None 0 2
720.1.be \(\chi_{720}(467, \cdot)\) None 0 2
720.1.bf \(\chi_{720}(397, \cdot)\) None 0 2
720.1.bh \(\chi_{720}(433, \cdot)\) None 0 2
720.1.bk \(\chi_{720}(143, \cdot)\) 720.1.bk.a 4 2
720.1.bn \(\chi_{720}(269, \cdot)\) None 0 2
720.1.bo \(\chi_{720}(91, \cdot)\) None 0 2
720.1.bp \(\chi_{720}(439, \cdot)\) None 0 2
720.1.bq \(\chi_{720}(41, \cdot)\) None 0 2
720.1.bs \(\chi_{720}(401, \cdot)\) None 0 2
720.1.bu \(\chi_{720}(79, \cdot)\) 720.1.bu.a 4 2
720.1.bx \(\chi_{720}(329, \cdot)\) None 0 2
720.1.bz \(\chi_{720}(151, \cdot)\) None 0 2
720.1.cb \(\chi_{720}(31, \cdot)\) None 0 2
720.1.cd \(\chi_{720}(209, \cdot)\) None 0 2
720.1.cg \(\chi_{720}(211, \cdot)\) None 0 4
720.1.ch \(\chi_{720}(29, \cdot)\) None 0 4
720.1.cj \(\chi_{720}(97, \cdot)\) None 0 4
720.1.ck \(\chi_{720}(47, \cdot)\) None 0 4
720.1.cn \(\chi_{720}(133, \cdot)\) None 0 4
720.1.co \(\chi_{720}(203, \cdot)\) None 0 4
720.1.cr \(\chi_{720}(13, \cdot)\) None 0 4
720.1.cs \(\chi_{720}(83, \cdot)\) None 0 4
720.1.cv \(\chi_{720}(23, \cdot)\) None 0 4
720.1.cw \(\chi_{720}(313, \cdot)\) None 0 4
720.1.cy \(\chi_{720}(101, \cdot)\) None 0 4
720.1.cz \(\chi_{720}(139, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(720))\) into lower level spaces

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