Properties

Label 1344.2.k
Level $1344$
Weight $2$
Character orbit 1344.k
Rep. character $\chi_{1344}(1217,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $10$
Sturm bound $512$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1344.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(512\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(5\), \(43\)

Dimensions

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

Total New Old
Modular forms 280 68 212
Cusp forms 232 60 172
Eisenstein series 48 8 40

Trace form

\( 60q - 4q^{9} + O(q^{10}) \) \( 60q - 4q^{9} - 4q^{21} + 36q^{25} + 24q^{37} - 4q^{49} + 8q^{57} + 28q^{81} + 48q^{85} - 8q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1344, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1344.2.k.a \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-4\) \(q+\zeta_{6}q^{3}+(-2-\zeta_{6})q^{7}-3q^{9}+4\zeta_{6}q^{13}+\cdots\)
1344.2.k.b \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{6}q^{3}+(2-\zeta_{6})q^{7}-3q^{9}-4\zeta_{6}q^{13}+\cdots\)
1344.2.k.c \(4\) \(10.732\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(-4\) \(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
1344.2.k.d \(4\) \(10.732\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(1+\beta _{1}+\beta _{3})q^{7}+\cdots\)
1344.2.k.e \(8\) \(10.732\) 8.0.342102016.5 None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{3})q^{5}+(-1-\beta _{4}+\cdots)q^{7}+\cdots\)
1344.2.k.f \(8\) \(10.732\) 8.0.342102016.5 None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-1-\beta _{5})q^{7}+(-\beta _{5}+\cdots)q^{9}+\cdots\)
1344.2.k.g \(8\) \(10.732\) 8.0.49787136.1 \(\Q(\sqrt{-21}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-\beta _{5}q^{5}+\beta _{2}q^{7}-3q^{9}+\beta _{3}q^{11}+\cdots\)
1344.2.k.h \(8\) \(10.732\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{4}+\beta _{5})q^{3}+\beta _{7}q^{5}+(-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
1344.2.k.i \(8\) \(10.732\) 8.0.342102016.5 None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{4}q^{3}-\beta _{2}q^{5}+(1+\beta _{5}+\beta _{6}+\beta _{7})q^{7}+\cdots\)
1344.2.k.j \(8\) \(10.732\) 8.0.342102016.5 None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{3}q^{3}+(-\beta _{2}-\beta _{3})q^{5}+(1+\beta _{4}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)