Properties

Label 441.1.b
Level $441$
Weight $1$
Character orbit 441.b
Rep. character $\chi_{441}(197,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $56$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 441.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(56\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(441, [\chi])\).

Total New Old
Modular forms 18 2 16
Cusp forms 2 2 0
Eisenstein series 16 0 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q - 2q^{4} + O(q^{10}) \) \( 2q - 2q^{4} - 2q^{16} - 4q^{22} + 2q^{25} + 4q^{46} + 4q^{58} + 2q^{64} - 4q^{67} + 4q^{79} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(441, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
441.1.b.a \(2\) \(0.220\) \(\Q(\sqrt{-2}) \) \(D_{4}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}-q^{4}-\beta q^{11}-q^{16}-2q^{22}+\cdots\)