Properties

Label 240.1
Level 240
Weight 1
Dimension 4
Nonzero newspaces 1
Newforms 1
Sturm bound 3072
Trace bound 0

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Defining parameters

Level: \( N \) = \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(3072\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(240))\).

Total New Old
Modular forms 234 30 204
Cusp forms 10 4 6
Eisenstein series 224 26 198

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\(4q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut -\mathstrut 4q^{15} \) \(\mathstrut -\mathstrut 4q^{16} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut -\mathstrut 4q^{34} \) \(\mathstrut -\mathstrut 4q^{36} \) \(\mathstrut -\mathstrut 4q^{46} \) \(\mathstrut -\mathstrut 4q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut +\mathstrut 4q^{54} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut +\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 4q^{76} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut -\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 4q^{94} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(240))\)

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
240.1.c \(\chi_{240}(209, \cdot)\) None 0 1
240.1.e \(\chi_{240}(31, \cdot)\) None 0 1
240.1.g \(\chi_{240}(151, \cdot)\) None 0 1
240.1.i \(\chi_{240}(89, \cdot)\) None 0 1
240.1.j \(\chi_{240}(79, \cdot)\) None 0 1
240.1.l \(\chi_{240}(161, \cdot)\) None 0 1
240.1.n \(\chi_{240}(41, \cdot)\) None 0 1
240.1.p \(\chi_{240}(199, \cdot)\) None 0 1
240.1.q \(\chi_{240}(19, \cdot)\) None 0 2
240.1.r \(\chi_{240}(101, \cdot)\) None 0 2
240.1.u \(\chi_{240}(23, \cdot)\) None 0 2
240.1.x \(\chi_{240}(73, \cdot)\) None 0 2
240.1.z \(\chi_{240}(83, \cdot)\) None 0 2
240.1.ba \(\chi_{240}(13, \cdot)\) None 0 2
240.1.bd \(\chi_{240}(203, \cdot)\) None 0 2
240.1.be \(\chi_{240}(133, \cdot)\) None 0 2
240.1.bg \(\chi_{240}(97, \cdot)\) None 0 2
240.1.bj \(\chi_{240}(47, \cdot)\) None 0 2
240.1.bm \(\chi_{240}(29, \cdot)\) 240.1.bm.a 4 2
240.1.bn \(\chi_{240}(91, \cdot)\) None 0 2

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(240))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(240)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)