Properties

Label 1344.2.j
Level 1344
Weight 2
Character orbit j
Rep. character \(\chi_{1344}(1247,\cdot)\)
Character field \(\Q\)
Dimension 48
Newforms 9
Sturm bound 512
Trace bound 23

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Defining parameters

Level: \( N \) = \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1344.j (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 24 \)
Character field: \(\Q\)
Newforms: \( 9 \)
Sturm bound: \(512\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(5\), \(19\), \(23\), \(47\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1344, [\chi])\).

Total New Old
Modular forms 280 48 232
Cusp forms 232 48 184
Eisenstein series 48 0 48

Trace form

\(48q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(48q \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut +\mathstrut 48q^{33} \) \(\mathstrut -\mathstrut 48q^{49} \) \(\mathstrut +\mathstrut 48q^{57} \) \(\mathstrut -\mathstrut 48q^{81} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1344, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1344.2.j.a \(4\) \(10.732\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{3}+\zeta_{12}q^{7}-3q^{9}+2\zeta_{12}^{2}q^{11}+\cdots\)
1344.2.j.b \(4\) \(10.732\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{7}-3q^{9}+2\zeta_{12}^{2}q^{11}+\cdots\)
1344.2.j.c \(4\) \(10.732\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}-\beta _{2}q^{7}+3\beta _{2}q^{9}+\cdots\)
1344.2.j.d \(4\) \(10.732\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}+3\beta _{2}q^{9}+\cdots\)
1344.2.j.e \(4\) \(10.732\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{3}q^{3}-2\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}+\cdots\)
1344.2.j.f \(4\) \(10.732\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{3}-2\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}+\cdots\)
1344.2.j.g \(8\) \(10.732\) \(\Q(\zeta_{24})\) None \(0\) \(-8\) \(0\) \(0\) \(q+(-1+\zeta_{24}^{2})q^{3}+(-\zeta_{24}^{3}+\zeta_{24}^{6}+\cdots)q^{5}+\cdots\)
1344.2.j.h \(8\) \(10.732\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{4}-\beta _{5})q^{3}-\beta _{7}q^{5}+\beta _{1}q^{7}+(2+\cdots)q^{9}+\cdots\)
1344.2.j.i \(8\) \(10.732\) \(\Q(\zeta_{24})\) None \(0\) \(8\) \(0\) \(0\) \(q+(1-\zeta_{24}^{2})q^{3}+(-\zeta_{24}^{3}+\zeta_{24}^{6}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1344, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)