Properties

Label 196.1
Level 196
Weight 1
Dimension 3
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 2352
Trace bound 1

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Defining parameters

Level: \( N \) = \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(2352\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(196))\).

Total New Old
Modular forms 153 52 101
Cusp forms 3 3 0
Eisenstein series 150 49 101

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 0 0 0

Trace form

\( 3q - 3q^{8} + O(q^{10}) \) \( 3q - 3q^{8} - 6q^{29} + 3q^{36} + 3q^{50} + 3q^{64} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(196))\)

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
196.1.b \(\chi_{196}(97, \cdot)\) None 0 1
196.1.c \(\chi_{196}(99, \cdot)\) 196.1.c.a 1 1
196.1.g \(\chi_{196}(67, \cdot)\) 196.1.g.a 2 2
196.1.h \(\chi_{196}(117, \cdot)\) None 0 2
196.1.k \(\chi_{196}(15, \cdot)\) None 0 6
196.1.l \(\chi_{196}(13, \cdot)\) None 0 6
196.1.n \(\chi_{196}(5, \cdot)\) None 0 12
196.1.o \(\chi_{196}(11, \cdot)\) None 0 12