Properties

Label 288.1
Level 288
Weight 1
Dimension 8
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 4608
Trace bound 3

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Defining parameters

Level: \( N \) = \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(4608\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(288))\).

Total New Old
Modular forms 272 53 219
Cusp forms 16 8 8
Eisenstein series 256 45 211

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

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

Trace form

\( 8q + q^{3} + 2q^{5} - 5q^{9} + O(q^{10}) \) \( 8q + q^{3} + 2q^{5} - 5q^{9} - q^{11} - 2q^{13} - 2q^{17} + 2q^{19} + 2q^{21} - 3q^{25} - 2q^{27} - 2q^{29} - q^{33} - 4q^{37} - q^{41} - q^{43} - 2q^{45} - 3q^{49} - q^{51} + q^{57} - q^{59} + 2q^{61} + 2q^{65} - q^{67} + 2q^{69} - 2q^{73} + q^{75} - 2q^{77} + 3q^{81} + 2q^{83} + 4q^{85} + 4q^{89} + 2q^{93} - q^{97} + 2q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(288))\)

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
288.1.b \(\chi_{288}(271, \cdot)\) None 0 1
288.1.e \(\chi_{288}(161, \cdot)\) 288.1.e.a 2 1
288.1.g \(\chi_{288}(127, \cdot)\) None 0 1
288.1.h \(\chi_{288}(17, \cdot)\) None 0 1
288.1.j \(\chi_{288}(89, \cdot)\) None 0 2
288.1.m \(\chi_{288}(55, \cdot)\) None 0 2
288.1.n \(\chi_{288}(113, \cdot)\) None 0 2
288.1.o \(\chi_{288}(31, \cdot)\) 288.1.o.a 4 2
288.1.q \(\chi_{288}(65, \cdot)\) None 0 2
288.1.t \(\chi_{288}(79, \cdot)\) 288.1.t.a 2 2
288.1.u \(\chi_{288}(19, \cdot)\) None 0 4
288.1.x \(\chi_{288}(53, \cdot)\) None 0 4
288.1.z \(\chi_{288}(7, \cdot)\) None 0 4
288.1.ba \(\chi_{288}(41, \cdot)\) None 0 4
288.1.bd \(\chi_{288}(43, \cdot)\) None 0 8
288.1.be \(\chi_{288}(5, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(288))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(288)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)