Properties

Label 3072.1.i
Level $3072$
Weight $1$
Character orbit 3072.i
Rep. character $\chi_{3072}(257,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $24$
Newform subspaces $8$
Sturm bound $512$
Trace bound $33$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 3072 = 2^{10} \cdot 3 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3072.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 8 \)
Sturm bound: \(512\)
Trace bound: \(33\)

Dimensions

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

Total New Old
Modular forms 144 40 104
Cusp forms 48 24 24
Eisenstein series 96 16 80

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 24 0 0 0

Trace form

\( 24q + O(q^{10}) \) \( 24q + 8q^{49} - 8q^{81} - 16q^{97} + O(q^{100}) \)

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.i.a \(2\) \(1.533\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}+q^{9}+(-1+i)q^{11}-iq^{17}+\cdots\)
3072.1.i.b \(2\) \(1.533\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-q^{9}+(-1+i)q^{11}+iq^{17}+\cdots\)
3072.1.i.c \(2\) \(1.533\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-q^{9}+(1-i)q^{11}+iq^{17}+\cdots\)
3072.1.i.d \(2\) \(1.533\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}+q^{9}+(1-i)q^{11}-iq^{17}+(-1+\cdots)q^{19}+\cdots\)
3072.1.i.e \(4\) \(1.533\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{8}^{3}q^{3}+(-1-\zeta_{8}^{2})q^{5}+(\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{7}+\cdots\)
3072.1.i.f \(4\) \(1.533\) \(\Q(\zeta_{8})\) \(D_{2}\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{9}-\zeta_{8}q^{11}-\zeta_{8}^{2}q^{25}+\cdots\)
3072.1.i.g \(4\) \(1.533\) \(\Q(\zeta_{8})\) \(D_{2}\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{6}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{9}-\zeta_{8}q^{19}-\zeta_{8}^{2}q^{25}+\cdots\)
3072.1.i.h \(4\) \(1.533\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{8}^{3}q^{3}+(1+\zeta_{8}^{2})q^{5}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots\)

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

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