Properties

Label 363.1
Level 363
Weight 1
Dimension 5
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 9680
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(9680\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(363))\).

Total New Old
Modular forms 325 146 179
Cusp forms 5 5 0
Eisenstein series 320 141 179

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 5 0 0 0

Trace form

\( 5q + O(q^{10}) \) \( 5q - 5q^{12} - 10q^{67} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(363))\)

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
363.1.b \(\chi_{363}(122, \cdot)\) 363.1.b.a 1 1
363.1.c \(\chi_{363}(241, \cdot)\) None 0 1
363.1.g \(\chi_{363}(40, \cdot)\) None 0 4
363.1.h \(\chi_{363}(245, \cdot)\) 363.1.h.a 4 4
363.1.k \(\chi_{363}(10, \cdot)\) None 0 10
363.1.l \(\chi_{363}(23, \cdot)\) None 0 10
363.1.n \(\chi_{363}(5, \cdot)\) None 0 40
363.1.o \(\chi_{363}(7, \cdot)\) None 0 40