Properties

Label 216.1
Level 216
Weight 1
Dimension 10
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 2592
Trace bound 2

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(2592\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(216))\).

Total New Old
Modular forms 196 42 154
Cusp forms 16 10 6
Eisenstein series 180 32 148

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 10 0 0 0

Trace form

\( 10q + q^{2} + q^{4} - 2q^{7} - 5q^{8} + O(q^{10}) \) \( 10q + q^{2} + q^{4} - 2q^{7} - 5q^{8} - 2q^{10} - 4q^{11} - 3q^{12} + q^{16} + 2q^{17} + 6q^{18} - 2q^{19} - 4q^{22} - q^{25} - 3q^{27} - 2q^{28} - 2q^{31} + q^{32} - 3q^{33} - 2q^{34} + 5q^{38} - 2q^{40} - 4q^{41} - 2q^{43} + 2q^{44} - q^{49} + q^{50} + 6q^{51} + 2q^{55} - 3q^{57} + 4q^{58} + 5q^{59} + q^{64} - 2q^{67} + 5q^{68} + 2q^{70} - 4q^{73} + 7q^{76} + 4q^{79} - 2q^{82} + 2q^{83} - 4q^{86} + 5q^{88} - q^{89} + 6q^{96} - 4q^{97} - 5q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(216))\)

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
216.1.b \(\chi_{216}(163, \cdot)\) None 0 1
216.1.e \(\chi_{216}(161, \cdot)\) None 0 1
216.1.g \(\chi_{216}(55, \cdot)\) None 0 1
216.1.h \(\chi_{216}(53, \cdot)\) 216.1.h.a 1 1
216.1.h.b 1
216.1.j \(\chi_{216}(125, \cdot)\) None 0 2
216.1.k \(\chi_{216}(127, \cdot)\) None 0 2
216.1.m \(\chi_{216}(17, \cdot)\) None 0 2
216.1.p \(\chi_{216}(19, \cdot)\) 216.1.p.a 2 2
216.1.r \(\chi_{216}(43, \cdot)\) 216.1.r.a 6 6
216.1.s \(\chi_{216}(7, \cdot)\) None 0 6
216.1.u \(\chi_{216}(41, \cdot)\) None 0 6
216.1.x \(\chi_{216}(5, \cdot)\) None 0 6

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(216))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(216)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 2}\)