Properties

Label 3072.1.h
Level $3072$
Weight $1$
Character orbit 3072.h
Rep. character $\chi_{3072}(2561,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $512$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3072 = 2^{10} \cdot 3 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3072.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(512\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 86 12 74
Cusp forms 38 4 34
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.h.a \(4\) \(1.533\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{3}+(\zeta_{8}-\zeta_{8}^{3})q^{7}-q^{9}+(\zeta_{8}+\cdots)q^{13}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3072, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1536, [\chi])\)\(^{\oplus 2}\)