Properties

Label 1344.2.b
Level 1344
Weight 2
Character orbit b
Rep. character \(\chi_{1344}(895,\cdot)\)
Character field \(\Q\)
Dimension 32
Newforms 8
Sturm bound 512
Trace bound 7

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Defining parameters

Level: \( N \) = \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1344.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 28 \)
Character field: \(\Q\)
Newforms: \( 8 \)
Sturm bound: \(512\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(19\)

Dimensions

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

Total New Old
Modular forms 280 32 248
Cusp forms 232 32 200
Eisenstein series 48 0 48

Trace form

\(32q \) \(\mathstrut +\mathstrut 32q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(32q \) \(\mathstrut +\mathstrut 32q^{9} \) \(\mathstrut -\mathstrut 8q^{21} \) \(\mathstrut -\mathstrut 32q^{25} \) \(\mathstrut +\mathstrut 16q^{29} \) \(\mathstrut -\mathstrut 16q^{53} \) \(\mathstrut -\mathstrut 48q^{77} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut +\mathstrut 96q^{85} \) \(\mathstrut +\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.b.a \(2\) \(10.732\) \(\Q(\sqrt{-6}) \) None \(0\) \(-2\) \(0\) \(-2\) \(q-q^{3}+\beta q^{5}+(-1-\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
1344.2.b.b \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(4\) \(q-q^{3}+(2-\zeta_{6})q^{7}+q^{9}+2\zeta_{6}q^{11}+\cdots\)
1344.2.b.c \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(-4\) \(q+q^{3}+(-2+\zeta_{6})q^{7}+q^{9}-2\zeta_{6}q^{11}+\cdots\)
1344.2.b.d \(2\) \(10.732\) \(\Q(\sqrt{-6}) \) None \(0\) \(2\) \(0\) \(2\) \(q+q^{3}+\beta q^{5}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
1344.2.b.e \(4\) \(10.732\) 4.0.2312.1 None \(0\) \(-4\) \(0\) \(-2\) \(q-q^{3}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1344.2.b.f \(4\) \(10.732\) 4.0.2312.1 None \(0\) \(4\) \(0\) \(2\) \(q+q^{3}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
1344.2.b.g \(8\) \(10.732\) 8.0.836829184.2 None \(0\) \(-8\) \(0\) \(4\) \(q-q^{3}-\beta _{1}q^{5}-\beta _{4}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
1344.2.b.h \(8\) \(10.732\) 8.0.836829184.2 None \(0\) \(8\) \(0\) \(-4\) \(q+q^{3}-\beta _{1}q^{5}+\beta _{4}q^{7}+q^{9}+(\beta _{2}+\beta _{4}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)