Properties

Label 441.1.m
Level $441$
Weight $1$
Character orbit 441.m
Rep. character $\chi_{441}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
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.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
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 34 6 28
Cusp forms 2 2 0
Eisenstein series 32 4 28

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

\( 2 q + q^{4} + O(q^{10}) \) \( 2 q + q^{4} - q^{16} - q^{25} + 2 q^{37} - 4 q^{43} - 2 q^{64} - 2 q^{67} - 2 q^{79} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
441.1.m.a 441.m 7.d $2$ $0.220$ \(\Q(\sqrt{-3}) \) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{4}-\zeta_{6}q^{16}+\zeta_{6}^{2}q^{25}+\zeta_{6}q^{37}+\cdots\)