Properties

Label 360.1
Level 360
Weight 1
Dimension 6
Nonzero newspaces 2
Newforms 3
Sturm bound 6912
Trace bound 1

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Defining parameters

Level: \( N \) = \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 3 \)
Sturm bound: \(6912\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(360))\).

Total New Old
Modular forms 418 60 358
Cusp forms 34 6 28
Eisenstein series 384 54 330

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\(6q \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut -\mathstrut 4q^{28} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut -\mathstrut 4q^{46} \) \(\mathstrut -\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 4q^{58} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut +\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 4q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(360))\)

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
360.1.c \(\chi_{360}(89, \cdot)\) None 0 1
360.1.e \(\chi_{360}(271, \cdot)\) None 0 1
360.1.g \(\chi_{360}(91, \cdot)\) None 0 1
360.1.i \(\chi_{360}(269, \cdot)\) None 0 1
360.1.j \(\chi_{360}(199, \cdot)\) None 0 1
360.1.l \(\chi_{360}(161, \cdot)\) None 0 1
360.1.n \(\chi_{360}(341, \cdot)\) None 0 1
360.1.p \(\chi_{360}(19, \cdot)\) 360.1.p.a 1 1
360.1.p.b 1
360.1.r \(\chi_{360}(107, \cdot)\) None 0 2
360.1.u \(\chi_{360}(37, \cdot)\) 360.1.u.a 4 2
360.1.v \(\chi_{360}(73, \cdot)\) None 0 2
360.1.y \(\chi_{360}(143, \cdot)\) None 0 2
360.1.z \(\chi_{360}(139, \cdot)\) None 0 2
360.1.ba \(\chi_{360}(101, \cdot)\) None 0 2
360.1.bc \(\chi_{360}(41, \cdot)\) None 0 2
360.1.be \(\chi_{360}(79, \cdot)\) None 0 2
360.1.bh \(\chi_{360}(29, \cdot)\) None 0 2
360.1.bj \(\chi_{360}(211, \cdot)\) None 0 2
360.1.bl \(\chi_{360}(31, \cdot)\) None 0 2
360.1.bn \(\chi_{360}(209, \cdot)\) None 0 2
360.1.bp \(\chi_{360}(97, \cdot)\) None 0 4
360.1.bq \(\chi_{360}(23, \cdot)\) None 0 4
360.1.bt \(\chi_{360}(83, \cdot)\) None 0 4
360.1.bu \(\chi_{360}(13, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(360))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(360)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 2}\)