Properties

Label 1344.2.i
Level 1344
Weight 2
Character orbit i
Rep. character \(\chi_{1344}(545,\cdot)\)
Character field \(\Q\)
Dimension 64
Newforms 7
Sturm bound 512
Trace bound 21

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Defining parameters

Level: \( N \) = \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1344.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 168 \)
Character field: \(\Q\)
Newforms: \( 7 \)
Sturm bound: \(512\)
Trace bound: \(21\)
Distinguishing \(T_p\): \(5\), \(13\), \(19\), \(29\)

Dimensions

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

Total New Old
Modular forms 280 64 216
Cusp forms 232 64 168
Eisenstein series 48 0 48

Trace form

\(64q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut -\mathstrut 64q^{25} \) \(\mathstrut -\mathstrut 16q^{49} \) \(\mathstrut -\mathstrut 96q^{81} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.i.a \(4\) \(10.732\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+(\zeta_{12}-\zeta_{12}^{3})q^{7}+3q^{9}+\cdots\)
1344.2.i.b \(4\) \(10.732\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+(-\zeta_{12}+\zeta_{12}^{3})q^{7}+3q^{9}+\cdots\)
1344.2.i.c \(8\) \(10.732\) 8.0.49787136.1 \(\Q(\sqrt{-42}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+\beta _{3}q^{7}-3q^{9}+\beta _{7}q^{13}+\cdots\)
1344.2.i.d \(8\) \(10.732\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{3}+(-2\beta _{2}-\beta _{7})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
1344.2.i.e \(8\) \(10.732\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{3}+(-2\beta _{2}-\beta _{7})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
1344.2.i.f \(16\) \(10.732\) 16.0.\(\cdots\).1 None \(0\) \(-16\) \(0\) \(0\) \(q+(-1+\beta _{6})q^{3}+\beta _{5}q^{5}-\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots\)
1344.2.i.g \(16\) \(10.732\) 16.0.\(\cdots\).1 None \(0\) \(16\) \(0\) \(0\) \(q+(1+\beta _{6})q^{3}+\beta _{5}q^{5}+\beta _{3}q^{7}+(-1+\cdots)q^{9}+\cdots\)

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

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