Properties

Label 1008.2.s
Level $1008$
Weight $2$
Character orbit 1008.s
Rep. character $\chi_{1008}(289,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $38$
Newform subspaces $18$
Sturm bound $384$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.s (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 18 \)
Sturm bound: \(384\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\)

Dimensions

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

Total New Old
Modular forms 432 42 390
Cusp forms 336 38 298
Eisenstein series 96 4 92

Trace form

\( 38q + q^{5} + O(q^{10}) \) \( 38q + q^{5} - 3q^{11} - 4q^{13} + q^{17} + 9q^{19} - 9q^{23} - 20q^{25} + 4q^{29} - 9q^{31} - 15q^{35} + 3q^{37} - 4q^{41} + 16q^{43} + 15q^{47} + 6q^{49} + 9q^{53} + 22q^{55} - 11q^{59} + 3q^{61} + 18q^{65} + 7q^{67} + 8q^{71} + 11q^{73} - 25q^{77} + 13q^{79} + 64q^{83} - 10q^{85} - 3q^{89} + 52q^{91} + 45q^{95} + 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

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

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

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