Properties

Label 441.1.v
Level $441$
Weight $1$
Character orbit 441.v
Rep. character $\chi_{441}(55,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $6$
Newform subspaces $1$
Sturm bound $56$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 441.v (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{14})\)
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 30 12 18
Cusp forms 6 6 0
Eisenstein series 24 6 18

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6q + q^{4} + q^{7} + O(q^{10}) \) \( 6q + q^{4} + q^{7} - q^{16} - q^{25} - q^{28} - 5q^{37} + 2q^{43} - q^{49} - 7q^{52} - 7q^{61} + q^{64} - 2q^{67} - 2q^{79} + O(q^{100}) \)

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.v.a \(6\) \(0.220\) \(\Q(\zeta_{14})\) \(D_{14}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-\zeta_{14}^{4}q^{4}-\zeta_{14}^{2}q^{7}+(\zeta_{14}-\zeta_{14}^{3}+\cdots)q^{13}+\cdots\)