Properties

Label 882.2.h
Level $882$
Weight $2$
Character orbit 882.h
Rep. character $\chi_{882}(67,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $20$
Sturm bound $336$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.h (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 20 \)
Sturm bound: \(336\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(882, [\chi])\).

Total New Old
Modular forms 368 80 288
Cusp forms 304 80 224
Eisenstein series 64 0 64

Trace form

\( 80q - 40q^{4} - 8q^{5} + 4q^{6} + 6q^{9} + O(q^{10}) \) \( 80q - 40q^{4} - 8q^{5} + 4q^{6} + 6q^{9} + 16q^{11} - 2q^{13} - 14q^{15} - 40q^{16} + 14q^{17} - 20q^{18} + 4q^{19} + 4q^{20} + 4q^{23} - 2q^{24} + 80q^{25} + 16q^{26} + 18q^{29} - 18q^{30} - 2q^{31} - 2q^{33} + 12q^{36} - 2q^{37} - 24q^{38} + 2q^{39} + 6q^{41} - 2q^{43} - 8q^{44} + 28q^{45} + 6q^{46} + 6q^{47} - 4q^{51} + 4q^{52} - 32q^{53} - 2q^{54} + 12q^{55} - 30q^{57} + 12q^{58} + 22q^{59} - 14q^{60} - 8q^{61} - 44q^{62} + 80q^{64} - 2q^{65} - 8q^{66} - 14q^{67} - 28q^{68} - 38q^{69} - 76q^{71} + 4q^{72} + 28q^{73} - 12q^{74} + 74q^{75} + 4q^{76} - 56q^{78} - 32q^{79} + 4q^{80} + 26q^{81} - 16q^{83} - 24q^{85} + 40q^{86} + 56q^{87} + 36q^{89} - 2q^{90} - 2q^{92} - 86q^{93} - 12q^{94} - 42q^{95} - 2q^{96} - 2q^{97} + 34q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(882, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
882.2.h.a \(2\) \(7.043\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(-2\) \(0\) \(q+(-1+\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.h.b \(2\) \(7.043\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(0\) \(q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.h.c \(2\) \(7.043\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(0\) \(q+(-1+\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.h.d \(2\) \(7.043\) \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(2\) \(0\) \(q+(-1+\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.h.e \(2\) \(7.043\) \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(6\) \(0\) \(q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.h.f \(2\) \(7.043\) \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(6\) \(0\) \(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.h.g \(2\) \(7.043\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-4\) \(0\) \(q+(1-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.h.h \(2\) \(7.043\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(4\) \(0\) \(q+(1-\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.h.i \(2\) \(7.043\) \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(-6\) \(0\) \(q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.h.j \(2\) \(7.043\) \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(-6\) \(0\) \(q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.h.k \(4\) \(7.043\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(-2\) \(4\) \(0\) \(q+(-1+\beta _{2})q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+\cdots\)
882.2.h.l \(4\) \(7.043\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(2\) \(-4\) \(0\) \(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
882.2.h.m \(4\) \(7.043\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(-1\) \(6\) \(0\) \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-1+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)
882.2.h.n \(4\) \(7.043\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(1\) \(-6\) \(0\) \(q+(1-\beta _{2})q^{2}+(\beta _{2}+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
882.2.h.o \(6\) \(7.043\) 6.0.309123.1 None \(-3\) \(-4\) \(-10\) \(0\) \(q+(-1-\beta _{4})q^{2}+(\beta _{2}+\beta _{3}-\beta _{5})q^{3}+\cdots\)
882.2.h.p \(6\) \(7.043\) 6.0.309123.1 None \(3\) \(-2\) \(2\) \(0\) \(q-\beta _{4}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)
882.2.h.q \(8\) \(7.043\) \(\Q(\zeta_{24})\) None \(-4\) \(0\) \(0\) \(0\) \(q+(-1+\zeta_{24})q^{2}+(\zeta_{24}^{3}+\zeta_{24}^{6})q^{3}+\cdots\)
882.2.h.r \(8\) \(7.043\) 8.0.3317760000.3 None \(-4\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+(\beta _{1}-\beta _{3}-\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)
882.2.h.s \(8\) \(7.043\) 8.0.\(\cdots\).2 None \(4\) \(0\) \(0\) \(0\) \(q+(1+\beta _{4})q^{2}+(\beta _{3}-\beta _{6})q^{3}+\beta _{4}q^{4}+\cdots\)
882.2.h.t \(8\) \(7.043\) \(\Q(\zeta_{24})\) None \(4\) \(0\) \(0\) \(0\) \(q+(1-\zeta_{24})q^{2}+(-\zeta_{24}^{5}+\zeta_{24}^{7})q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(882, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)