Properties

Label 287.1
Level 287
Weight 1
Dimension 6
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 6720
Trace bound 0

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 287 = 7 \cdot 41 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(6720\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(287))\).

Total New Old
Modular forms 246 200 46
Cusp forms 6 6 0
Eisenstein series 240 194 46

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

\( 6q - 2q^{2} + 4q^{4} - 4q^{8} + 4q^{9} + O(q^{10}) \) \( 6q - 2q^{2} + 4q^{4} - 4q^{8} + 4q^{9} + 2q^{16} - 6q^{18} - 2q^{21} - 2q^{23} + 6q^{25} - 6q^{32} - 2q^{36} - 2q^{37} - 4q^{39} - 4q^{42} - 2q^{43} - 4q^{46} + 6q^{49} - 2q^{50} - 4q^{51} - 4q^{57} + 2q^{72} + 10q^{74} + 6q^{78} + 2q^{81} + 8q^{84} - 4q^{86} - 2q^{91} + 8q^{92} - 2q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(287))\)

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
287.1.b \(\chi_{287}(83, \cdot)\) None 0 1
287.1.d \(\chi_{287}(286, \cdot)\) 287.1.d.a 3 1
287.1.d.b 3
287.1.g \(\chi_{287}(132, \cdot)\) None 0 2
287.1.i \(\chi_{287}(40, \cdot)\) None 0 2
287.1.k \(\chi_{287}(124, \cdot)\) None 0 2
287.1.m \(\chi_{287}(85, \cdot)\) None 0 4
287.1.o \(\chi_{287}(139, \cdot)\) None 0 4
287.1.p \(\chi_{287}(146, \cdot)\) None 0 4
287.1.q \(\chi_{287}(73, \cdot)\) None 0 4
287.1.t \(\chi_{287}(20, \cdot)\) None 0 8
287.1.v \(\chi_{287}(44, \cdot)\) None 0 8
287.1.x \(\chi_{287}(31, \cdot)\) None 0 8
287.1.y \(\chi_{287}(10, \cdot)\) None 0 8
287.1.ba \(\chi_{287}(15, \cdot)\) None 0 16
287.1.bd \(\chi_{287}(5, \cdot)\) None 0 16
287.1.bf \(\chi_{287}(11, \cdot)\) None 0 32