Properties

Label 3072.1.e
Level $3072$
Weight $1$
Character orbit 3072.e
Rep. character $\chi_{3072}(1025,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $512$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 3072 = 2^{10} \cdot 3 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3072.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(512\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3072, [\chi])\).

Total New Old
Modular forms 80 12 68
Cusp forms 32 4 28
Eisenstein series 48 8 40

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4q + 4q^{9} + O(q^{10}) \) \( 4q + 4q^{9} + 4q^{25} + 4q^{49} + 4q^{81} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3072, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3072.1.e.a \(2\) \(1.533\) \(\Q(\sqrt{2}) \) \(D_{4}\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}-\beta q^{7}+q^{9}-\beta q^{13}+\beta q^{21}+\cdots\)
3072.1.e.b \(2\) \(1.533\) \(\Q(\sqrt{2}) \) \(D_{4}\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}-\beta q^{7}+q^{9}+\beta q^{13}-\beta q^{21}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3072, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3072, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1536, [\chi])\)\(^{\oplus 2}\)