Properties

Label 720.1
Level 720
Weight 1
Dimension 13
Nonzero newspaces 4
Newforms 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: \( 4 \)
Newforms: \( 4 \)
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

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

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 the 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

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