Properties

Label 882.2.e
Level $882$
Weight $2$
Character orbit 882.e
Rep. character $\chi_{882}(373,\cdot)$
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.e (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

\( 80q + 80q^{4} + 4q^{5} + 4q^{6} + 12q^{9} + O(q^{10}) \) \( 80q + 80q^{4} + 4q^{5} + 4q^{6} + 12q^{9} - 8q^{11} - 2q^{13} - 14q^{15} + 80q^{16} + 14q^{17} + 16q^{18} + 4q^{19} + 4q^{20} - 2q^{23} + 4q^{24} - 40q^{25} + 16q^{26} + 18q^{29} + 4q^{31} + 40q^{33} + 12q^{36} - 2q^{37} + 12q^{38} - 16q^{39} + 6q^{41} - 2q^{43} - 8q^{44} - 38q^{45} + 6q^{46} - 12q^{47} - 34q^{51} - 2q^{52} - 32q^{53} - 14q^{54} + 12q^{55} - 30q^{57} - 6q^{58} - 44q^{59} - 14q^{60} + 16q^{61} - 44q^{62} + 80q^{64} + 4q^{65} + 16q^{66} + 28q^{67} + 14q^{68} - 38q^{69} - 76q^{71} + 16q^{72} + 28q^{73} + 6q^{74} - 76q^{75} + 4q^{76} - 56q^{78} + 64q^{79} + 4q^{80} - 4q^{81} - 16q^{83} - 24q^{85} - 20q^{86} - 4q^{87} + 36q^{89} - 2q^{90} - 2q^{92} + 70q^{93} + 24q^{94} + 84q^{95} + 4q^{96} - 2q^{97} + 34q^{99} + O(q^{100}) \)

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

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

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