Properties

Label 1008.2.cs
Level $1008$
Weight $2$
Character orbit 1008.cs
Rep. character $\chi_{1008}(271,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $40$
Newform subspaces $17$
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.cs (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 17 \)
Sturm bound: \(384\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\), \(19\)

Dimensions

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

Total New Old
Modular forms 432 40 392
Cusp forms 336 40 296
Eisenstein series 96 0 96

Trace form

\( 40q + O(q^{10}) \) \( 40q + 32q^{25} + 24q^{29} + 4q^{37} + 16q^{49} + 12q^{53} + 36q^{61} + 36q^{65} + 12q^{73} + 48q^{77} + 24q^{85} + 36q^{89} + O(q^{100}) \)

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.cs.a \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-6\) \(-1\) \(q+(-4+2\zeta_{6})q^{5}+(-2+3\zeta_{6})q^{7}+\cdots\)
1008.2.cs.b \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-6\) \(1\) \(q+(-4+2\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+(2+\cdots)q^{11}+\cdots\)
1008.2.cs.c \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(-4\) \(q+(-2+\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+(-1+\cdots)q^{11}+\cdots\)
1008.2.cs.d \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(-1\) \(q+(-2+\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}+(1+\zeta_{6})q^{11}+\cdots\)
1008.2.cs.e \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(1\) \(q+(-2+\zeta_{6})q^{5}+(-1+3\zeta_{6})q^{7}+(-1+\cdots)q^{11}+\cdots\)
1008.2.cs.f \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(4\) \(q+(-2+\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+(1+\zeta_{6})q^{11}+\cdots\)
1008.2.cs.g \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-5\) \(q+(-2-\zeta_{6})q^{7}+(-3+6\zeta_{6})q^{13}+\cdots\)
1008.2.cs.h \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-1\) \(q+(-2+3\zeta_{6})q^{7}+(1-2\zeta_{6})q^{13}+7\zeta_{6}q^{19}+\cdots\)
1008.2.cs.i \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1\) \(q+(2-3\zeta_{6})q^{7}+(1-2\zeta_{6})q^{13}-7\zeta_{6}q^{19}+\cdots\)
1008.2.cs.j \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(5\) \(q+(2+\zeta_{6})q^{7}+(-3+6\zeta_{6})q^{13}+\zeta_{6}q^{19}+\cdots\)
1008.2.cs.k \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(-5\) \(q+(2-\zeta_{6})q^{5}+(-3+\zeta_{6})q^{7}+(3+3\zeta_{6})q^{11}+\cdots\)
1008.2.cs.l \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(5\) \(q+(2-\zeta_{6})q^{5}+(3-\zeta_{6})q^{7}+(-3-3\zeta_{6})q^{11}+\cdots\)
1008.2.cs.m \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(6\) \(-1\) \(q+(4-2\zeta_{6})q^{5}+(-2+3\zeta_{6})q^{7}+(-2+\cdots)q^{11}+\cdots\)
1008.2.cs.n \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(6\) \(1\) \(q+(4-2\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+(2+2\zeta_{6})q^{11}+\cdots\)
1008.2.cs.o \(4\) \(8.049\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(-10\) \(q-\beta _{2}q^{5}+(-3-\beta _{1})q^{7}+(\beta _{2}-\beta _{3})q^{11}+\cdots\)
1008.2.cs.p \(4\) \(8.049\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(10\) \(q-\beta _{2}q^{5}+(3+\beta _{1})q^{7}+(-\beta _{2}+\beta _{3})q^{11}+\cdots\)
1008.2.cs.q \(4\) \(8.049\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(6\) \(0\) \(q+(1-\beta _{2})q^{5}+\beta _{3}q^{7}+(-\beta _{1}+\beta _{3})q^{11}+\cdots\)

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

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