Properties

Label 1008.3.cg
Level $1008$
Weight $3$
Character orbit 1008.cg
Rep. character $\chi_{1008}(145,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $78$
Newform subspaces $17$
Sturm bound $576$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1008.cg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 17 \)
Sturm bound: \(576\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1008, [\chi])\).

Total New Old
Modular forms 816 82 734
Cusp forms 720 78 642
Eisenstein series 96 4 92

Trace form

\( 78q + 3q^{5} - 6q^{7} + O(q^{10}) \) \( 78q + 3q^{5} - 6q^{7} - 9q^{11} + 3q^{17} - 45q^{19} + 7q^{23} + 182q^{25} + 36q^{29} - 45q^{31} - 147q^{35} - 25q^{37} - 108q^{43} - 147q^{47} - 98q^{49} - 47q^{53} + 93q^{59} + 69q^{61} - 32q^{65} + 33q^{67} - 100q^{71} - 123q^{73} + 89q^{77} - 71q^{79} - 86q^{85} + 75q^{89} + 336q^{91} + 117q^{95} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1008.3.cg.a \(2\) \(27.466\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-9\) \(-13\) \(q+(-6+3\zeta_{6})q^{5}+(-5-3\zeta_{6})q^{7}+\cdots\)
1008.3.cg.b \(2\) \(27.466\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(-13\) \(q+(-2+\zeta_{6})q^{5}+(-5-3\zeta_{6})q^{7}+(3+\cdots)q^{11}+\cdots\)
1008.3.cg.c \(2\) \(27.466\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(14\) \(q+(-2+\zeta_{6})q^{5}+7q^{7}+(-15+15\zeta_{6})q^{11}+\cdots\)
1008.3.cg.d \(2\) \(27.466\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-13\) \(q+(-8+3\zeta_{6})q^{7}+(-7+14\zeta_{6})q^{13}+\cdots\)
1008.3.cg.e \(2\) \(27.466\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(11\) \(q+(8-5\zeta_{6})q^{7}+(-15+30\zeta_{6})q^{13}+\cdots\)
1008.3.cg.f \(2\) \(27.466\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(6\) \(7\) \(q+(4-2\zeta_{6})q^{5}+7\zeta_{6}q^{7}+(-10+10\zeta_{6})q^{11}+\cdots\)
1008.3.cg.g \(2\) \(27.466\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(9\) \(7\) \(q+(6-3\zeta_{6})q^{5}+(7-7\zeta_{6})q^{7}+(11-11\zeta_{6})q^{11}+\cdots\)
1008.3.cg.h \(4\) \(27.466\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(-12\) \(10\) \(q+(-4-2\beta _{1}+\beta _{3})q^{5}+(-5\beta _{1}-\beta _{3})q^{7}+\cdots\)
1008.3.cg.i \(4\) \(27.466\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-14\) \(q+\beta _{3}q^{5}+7\beta _{1}q^{7}+(-2\beta _{2}-2\beta _{3})q^{11}+\cdots\)
1008.3.cg.j \(4\) \(27.466\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(0\) \(0\) \(0\) \(-14\) \(q+\beta _{2}q^{5}+(-7-7\beta _{1})q^{7}+(2\beta _{2}-\beta _{3})q^{11}+\cdots\)
1008.3.cg.k \(4\) \(27.466\) \(\Q(\sqrt{-3}, \sqrt{13})\) None \(0\) \(0\) \(0\) \(26\) \(q+(-\beta _{2}+\beta _{3})q^{5}+(8-3\beta _{1})q^{7}+\beta _{2}q^{11}+\cdots\)
1008.3.cg.l \(4\) \(27.466\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(6\) \(-8\) \(q+(2+\beta _{1}+2\beta _{3})q^{5}+(-1+2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1008.3.cg.m \(4\) \(27.466\) \(\Q(\sqrt{-3}, \sqrt{65})\) None \(0\) \(0\) \(9\) \(-2\) \(q+(2+\beta _{1}-\beta _{3})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
1008.3.cg.n \(8\) \(27.466\) 8.0.\(\cdots\).2 None \(0\) \(0\) \(-6\) \(4\) \(q+(-1-\beta _{4})q^{5}+(-\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
1008.3.cg.o \(8\) \(27.466\) 8.0.\(\cdots\).2 None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{5}q^{5}+(2-\beta _{1}-3\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
1008.3.cg.p \(8\) \(27.466\) 8.0.\(\cdots\).9 None \(0\) \(0\) \(6\) \(-8\) \(q+(1-\beta _{1}+\beta _{6})q^{5}+(-1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1008.3.cg.q \(16\) \(27.466\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-4\) \(q-\beta _{7}q^{5}+(-1+\beta _{2}-\beta _{5})q^{7}+(\beta _{4}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)