Properties

Label 882.2.bb
Level $882$
Weight $2$
Character orbit 882.bb
Rep. character $\chi_{882}(25,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $672$
Newform subspaces $2$
Sturm bound $336$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.bb (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{21})\)
Newform subspaces: \( 2 \)
Sturm bound: \(336\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 2064 672 1392
Cusp forms 1968 672 1296
Eisenstein series 96 0 96

Trace form

\( 672q - 112q^{4} + 4q^{5} - 10q^{6} + 2q^{7} - 10q^{9} + O(q^{10}) \) \( 672q - 112q^{4} + 4q^{5} - 10q^{6} + 2q^{7} - 10q^{9} - 2q^{13} - 2q^{14} - 6q^{15} - 112q^{16} + 14q^{17} + 8q^{18} + 4q^{19} + 4q^{20} + 20q^{21} - 78q^{23} + 4q^{24} + 56q^{25} + 16q^{26} + 84q^{27} + 2q^{28} - 26q^{29} - 8q^{30} + 4q^{31} + 40q^{33} + 14q^{35} - 10q^{36} + 26q^{37} + 12q^{38} - 16q^{39} + 6q^{41} - 86q^{42} - 2q^{43} + 214q^{45} - 78q^{46} + 30q^{47} - 4q^{49} + 8q^{50} + 6q^{51} + 26q^{52} - 156q^{53} - 14q^{54} - 30q^{55} - 2q^{56} - 48q^{57} + 78q^{58} - 44q^{59} - 6q^{60} - 82q^{61} - 44q^{62} - 24q^{63} - 112q^{64} - 28q^{65} + 16q^{66} + 28q^{67} - 42q^{68} - 66q^{69} + 18q^{70} + 14q^{71} + 8q^{72} + 28q^{73} + 6q^{74} - 34q^{75} + 4q^{76} - 50q^{77} - 8q^{78} + 16q^{79} - 24q^{80} - 46q^{81} + 376q^{83} - 22q^{84} - 4q^{86} - 60q^{87} + 106q^{89} + 82q^{90} + 16q^{91} + 6q^{92} + 76q^{93} + 24q^{94} + 52q^{95} + 4q^{96} - 2q^{97} - 32q^{98} - 190q^{99} + O(q^{100}) \)

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.bb.a \(336\) \(7.043\) None \(-56\) \(-5\) \(2\) \(0\)
882.2.bb.b \(336\) \(7.043\) None \(56\) \(5\) \(2\) \(2\)

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

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