Properties

Label 196.1.c
Level $196$
Weight $1$
Character orbit 196.c
Rep. character $\chi_{196}(99,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $28$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 196.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(28\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(196, [\chi])\).

Total New Old
Modular forms 9 6 3
Cusp forms 1 1 0
Eisenstein series 8 5 3

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\( q - q^{2} + q^{4} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + q^{4} - q^{8} + q^{9} + q^{16} - q^{18} - q^{25} - 2 q^{29} - q^{32} + q^{36} - 2 q^{37} + q^{50} + 2 q^{53} + 2 q^{58} + q^{64} - q^{72} + 2 q^{74} + q^{81} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(196, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
196.1.c.a $1$ $0.098$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{7}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots\)