Properties

Label 882.2.ba
Level $882$
Weight $2$
Character orbit 882.ba
Rep. character $\chi_{882}(43,\cdot)$
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.ba (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

\( 672 q + 56 q^{4} + 4 q^{5} + 20 q^{6} + 2 q^{7} - 10 q^{9} + O(q^{10}) \) \( 672 q + 56 q^{4} + 4 q^{5} + 20 q^{6} + 2 q^{7} - 10 q^{9} + 4 q^{13} - 2 q^{14} + 12 q^{15} + 56 q^{16} + 8 q^{17} + 8 q^{18} - 8 q^{19} + 4 q^{20} - 10 q^{21} + 30 q^{23} + 4 q^{24} + 56 q^{25} - 8 q^{26} - 6 q^{27} - 4 q^{28} + 10 q^{29} - 20 q^{30} + 4 q^{31} + 4 q^{33} + 8 q^{35} + 20 q^{36} + 20 q^{37} + 12 q^{38} - 28 q^{39} + 36 q^{41} + 70 q^{42} + 4 q^{43} - 86 q^{45} - 60 q^{46} + 30 q^{47} - 4 q^{49} - 16 q^{50} - 12 q^{51} - 10 q^{52} + 216 q^{53} - 20 q^{54} + 60 q^{55} - 2 q^{56} + 96 q^{57} - 30 q^{58} - 8 q^{59} - 24 q^{60} - 82 q^{61} - 8 q^{62} - 112 q^{64} - 28 q^{65} - 32 q^{66} + 28 q^{67} - 60 q^{68} + 24 q^{69} - 28 q^{71} + 8 q^{72} - 56 q^{73} - 12 q^{74} + 50 q^{75} + 4 q^{76} - 14 q^{77} + 16 q^{78} + 16 q^{79} + 48 q^{80} + 2 q^{81} - 128 q^{83} - 28 q^{84} + 8 q^{86} - 108 q^{87} - 140 q^{89} + 10 q^{90} - 32 q^{91} - 12 q^{92} + 70 q^{93} - 12 q^{94} + 52 q^{95} + 4 q^{96} + 4 q^{97} + 136 q^{98} + 380 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
882.2.ba.a 882.ba 441.aa $336$ $7.043$ None \(-28\) \(5\) \(2\) \(2\) $\mathrm{SU}(2)[C_{21}]$
882.2.ba.b 882.ba 441.aa $336$ $7.043$ None \(28\) \(-5\) \(2\) \(0\) $\mathrm{SU}(2)[C_{21}]$

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

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