Properties

Label 1764.1.co
Level $1764$
Weight $1$
Character orbit 1764.co
Rep. character $\chi_{1764}(73,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $12$
Newform subspaces $1$
Sturm bound $336$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1764.co (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 1 \)
Sturm bound: \(336\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1764, [\chi])\).

Total New Old
Modular forms 156 12 144
Cusp forms 12 12 0
Eisenstein series 144 0 144

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12q - q^{7} + O(q^{10}) \) \( 12q - q^{7} + 3q^{19} + q^{25} + 3q^{31} + 8q^{37} - 2q^{43} + q^{49} + 7q^{61} - q^{67} - 3q^{73} - q^{79} - 3q^{91} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1764, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1764.1.co.a \(12\) \(0.880\) \(\Q(\zeta_{21})\) \(D_{42}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-\zeta_{42}^{16}q^{7}+(-\zeta_{42}^{8}+\zeta_{42}^{10})q^{13}+\cdots\)