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Properties

Label 280.1
Level 280
Weight 1
Dimension 8
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 4608
Trace bound 4

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Defining parameters

Level: \( N \) = \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(4608\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(280))\).

Total New Old
Modular forms 310 68 242
Cusp forms 22 8 14
Eisenstein series 288 60 228

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q - 6 q^{4} - 6 q^{9} + O(q^{10}) \) \( 8 q - 6 q^{4} - 6 q^{9} - 2 q^{10} + 2 q^{11} + 2 q^{14} - 4 q^{15} + 2 q^{16} + 2 q^{19} - 2 q^{25} + 2 q^{26} - 4 q^{30} - 2 q^{35} + 8 q^{36} + 8 q^{39} - 2 q^{40} - 4 q^{41} + 2 q^{44} + 2 q^{46} - 4 q^{50} - 4 q^{59} + 4 q^{60} + 6 q^{65} + 2 q^{74} - 4 q^{76} - 6 q^{81} - 4 q^{89} + 4 q^{90} - 4 q^{91} + 2 q^{94} - 4 q^{95} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(280))\)

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
280.1.c \(\chi_{280}(69, \cdot)\) 280.1.c.a 4 1
280.1.d \(\chi_{280}(71, \cdot)\) None 0 1
280.1.f \(\chi_{280}(41, \cdot)\) None 0 1
280.1.i \(\chi_{280}(99, \cdot)\) None 0 1
280.1.j \(\chi_{280}(239, \cdot)\) None 0 1
280.1.m \(\chi_{280}(181, \cdot)\) None 0 1
280.1.o \(\chi_{280}(211, \cdot)\) None 0 1
280.1.p \(\chi_{280}(209, \cdot)\) None 0 1
280.1.r \(\chi_{280}(167, \cdot)\) None 0 2
280.1.u \(\chi_{280}(197, \cdot)\) None 0 2
280.1.v \(\chi_{280}(57, \cdot)\) None 0 2
280.1.y \(\chi_{280}(27, \cdot)\) None 0 2
280.1.z \(\chi_{280}(11, \cdot)\) None 0 2
280.1.bb \(\chi_{280}(89, \cdot)\) None 0 2
280.1.bd \(\chi_{280}(39, \cdot)\) None 0 2
280.1.be \(\chi_{280}(61, \cdot)\) None 0 2
280.1.bh \(\chi_{280}(201, \cdot)\) None 0 2
280.1.bi \(\chi_{280}(179, \cdot)\) 280.1.bi.a 2 2
280.1.bi.b 2
280.1.bk \(\chi_{280}(229, \cdot)\) None 0 2
280.1.bn \(\chi_{280}(151, \cdot)\) None 0 2
280.1.bp \(\chi_{280}(3, \cdot)\) None 0 4
280.1.bq \(\chi_{280}(137, \cdot)\) None 0 4
280.1.bt \(\chi_{280}(37, \cdot)\) None 0 4
280.1.bu \(\chi_{280}(47, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(280))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(280)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 2}\)