Properties

Label 1008.2.b
Level 1008
Weight 2
Character orbit b
Rep. character \(\chi_{1008}(559,\cdot)\)
Character field \(\Q\)
Dimension 20
Newforms 9
Sturm bound 384
Trace bound 19

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Defining parameters

Level: \( N \) = \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1008.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 28 \)
Character field: \(\Q\)
Newforms: \( 9 \)
Sturm bound: \(384\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(5\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1008, [\chi])\).

Total New Old
Modular forms 216 20 196
Cusp forms 168 20 148
Eisenstein series 48 0 48

Trace form

\(20q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 24q^{53} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 48q^{85} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1008, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1008.2.b.a \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+(-2+\zeta_{6})q^{7}-2\zeta_{6}q^{11}-4\zeta_{6}q^{17}+\cdots\)
1008.2.b.b \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+2\zeta_{6}q^{11}+\cdots\)
1008.2.b.c \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-4\) \(q+(-2+\zeta_{6})q^{7}-4\zeta_{6}q^{13}+8q^{19}+\cdots\)
1008.2.b.d \(2\) \(8.049\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+\beta q^{5}+(-1-\beta )q^{7}-\beta q^{11}-2\beta q^{13}+\cdots\)
1008.2.b.e \(2\) \(8.049\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\beta q^{5}+(1+\beta )q^{7}+\beta q^{11}-2\beta q^{13}+\cdots\)
1008.2.b.f \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(4\) \(q+(2-\zeta_{6})q^{7}-4\zeta_{6}q^{13}-8q^{19}+5q^{25}+\cdots\)
1008.2.b.g \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(4\) \(q-2\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}-2\zeta_{6}q^{11}+\cdots\)
1008.2.b.h \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(4\) \(q+(2+\zeta_{6})q^{7}-2\zeta_{6}q^{11}+4\zeta_{6}q^{17}+\cdots\)
1008.2.b.i \(4\) \(8.049\) \(\Q(\sqrt{-6}, \sqrt{7})\) \(\Q(\sqrt{-21}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{5}-\beta _{3}q^{7}-\beta _{2}q^{11}+3\beta _{1}q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)