Properties

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

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Defining parameters

Level: \( N \) = \( 240\( 240 = 2^{4} \cdot 3 \cdot 5 \) \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
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

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

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

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T^{4} \)
$3$ \( 1 + T^{4} \)
$5$ \( 1 + T^{4} \)
$7$ \( ( 1 + T^{2} )^{4} \)
$11$ \( ( 1 + T^{4} )^{2} \)
$13$ \( ( 1 + T^{4} )^{2} \)
$17$ \( ( 1 + T^{4} )^{2} \)
$19$ \( ( 1 + T )^{4}( 1 + T^{2} )^{2} \)
$23$ \( ( 1 + T^{4} )^{2} \)
$29$ \( ( 1 + T^{4} )^{2} \)
$31$ \( ( 1 + T^{2} )^{4} \)
$37$ \( ( 1 + T^{4} )^{2} \)
$41$ \( ( 1 + T^{2} )^{4} \)
$43$ \( ( 1 + T^{4} )^{2} \)
$47$ \( ( 1 + T^{4} )^{2} \)
$53$ \( ( 1 + T^{4} )^{2} \)
$59$ \( ( 1 + T^{4} )^{2} \)
$61$ \( ( 1 - T )^{4}( 1 + T^{2} )^{2} \)
$67$ \( ( 1 + T^{4} )^{2} \)
$71$ \( ( 1 + T^{2} )^{4} \)
$73$ \( ( 1 + T^{2} )^{4} \)
$79$ \( ( 1 - T )^{8} \)
$83$ \( ( 1 + T^{4} )^{2} \)
$89$ \( ( 1 + T^{2} )^{4} \)
$97$ \( ( 1 - T )^{4}( 1 + T )^{4} \)
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