Properties

Label 2016.2.s
Level $2016$
Weight $2$
Character orbit 2016.s
Rep. character $\chi_{2016}(289,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $24$
Sturm bound $768$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2016.s (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 24 \)
Sturm bound: \(768\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2016, [\chi])\).

Total New Old
Modular forms 832 80 752
Cusp forms 704 80 624
Eisenstein series 128 0 128

Trace form

\( 80q + O(q^{10}) \) \( 80q + 16q^{13} - 32q^{25} - 16q^{29} - 8q^{37} + 16q^{41} - 16q^{49} - 8q^{53} + 8q^{61} - 24q^{65} - 24q^{73} + 16q^{77} - 16q^{85} - 8q^{89} + 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2016, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2016.2.s.a \(2\) \(16.098\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-4\) \(-5\) \(q-4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
2016.2.s.b \(2\) \(16.098\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-4\) \(5\) \(q-4\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
2016.2.s.c \(2\) \(16.098\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(-1\) \(q-3\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\)
2016.2.s.d \(2\) \(16.098\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(1\) \(q-3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots\)
2016.2.s.e \(2\) \(16.098\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-5\) \(q+(-2-\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2016.2.s.f \(2\) \(16.098\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+(-2+3\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2016.2.s.g \(2\) \(16.098\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+(2-3\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+5q^{13}+\cdots\)
2016.2.s.h \(2\) \(16.098\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(5\) \(q+(2+\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+q^{13}+\cdots\)
2016.2.s.i \(2\) \(16.098\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-5\) \(q+\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots\)
2016.2.s.j \(2\) \(16.098\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(5\) \(q+\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+(1-\zeta_{6})q^{11}+\cdots\)
2016.2.s.k \(2\) \(16.098\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(-1\) \(q+3\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+(1-\zeta_{6})q^{11}+\cdots\)
2016.2.s.l \(2\) \(16.098\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(-1\) \(q+3\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots\)
2016.2.s.m \(2\) \(16.098\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(1\) \(q+3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\)
2016.2.s.n \(2\) \(16.098\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(1\) \(q+3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots\)
2016.2.s.o \(4\) \(16.098\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(-6\) \(0\) \(q+3\beta _{2}q^{5}+\beta _{3}q^{7}-\beta _{1}q^{11}-4q^{13}+\cdots\)
2016.2.s.p \(4\) \(16.098\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(0\) \(0\) \(-4\) \(0\) \(q-2\beta _{2}q^{5}+\beta _{3}q^{7}-3q^{13}+(2-2\beta _{2}+\cdots)q^{17}+\cdots\)
2016.2.s.q \(4\) \(16.098\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(2\) \(-4\) \(q+(1+2\beta _{1}+\beta _{2})q^{5}+(-1-2\beta _{1}-\beta _{3})q^{7}+\cdots\)
2016.2.s.r \(4\) \(16.098\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) \(q+(1-\zeta_{12}^{2})q^{5}+(2\zeta_{12}-3\zeta_{12}^{3})q^{7}+\cdots\)
2016.2.s.s \(4\) \(16.098\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(2\) \(4\) \(q+(1+2\beta _{1}+\beta _{2})q^{5}+(1+2\beta _{1}+\beta _{3})q^{7}+\cdots\)
2016.2.s.t \(4\) \(16.098\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(0\) \(0\) \(4\) \(0\) \(q+2\beta _{2}q^{5}+\beta _{3}q^{7}-3q^{13}+(-2+2\beta _{2}+\cdots)q^{17}+\cdots\)
2016.2.s.u \(6\) \(16.098\) 6.0.1156923.1 None \(0\) \(0\) \(0\) \(-3\) \(q+\beta _{4}q^{5}+(-1+\beta _{3}-\beta _{4})q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
2016.2.s.v \(6\) \(16.098\) 6.0.1156923.1 None \(0\) \(0\) \(0\) \(3\) \(q+\beta _{4}q^{5}+(1-\beta _{3}+\beta _{4})q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
2016.2.s.w \(8\) \(16.098\) 8.0.1445900625.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{5}+(\beta _{1}-\beta _{4}+\beta _{5})q^{7}+\beta _{6}q^{11}+\cdots\)
2016.2.s.x \(8\) \(16.098\) 8.0.1445900625.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{5}+(-\beta _{1}+\beta _{4}-\beta _{5})q^{7}-\beta _{6}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2016, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2016, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)