Properties

Label 441.2.ba
Level $441$
Weight $2$
Character orbit 441.ba
Rep. character $\chi_{441}(22,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $648$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.ba (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{21})\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(441, [\chi])\).

Total New Old
Modular forms 696 696 0
Cusp forms 648 648 0
Eisenstein series 48 48 0

Trace form

\( 648q - 5q^{2} - 10q^{3} + 47q^{4} - 9q^{5} - 34q^{6} - 7q^{7} - 28q^{8} + O(q^{10}) \) \( 648q - 5q^{2} - 10q^{3} + 47q^{4} - 9q^{5} - 34q^{6} - 7q^{7} - 28q^{8} - 28q^{10} - 5q^{11} + 5q^{12} - 7q^{13} - 38q^{14} - 22q^{15} + 47q^{16} - 16q^{17} - 46q^{18} - 44q^{19} - 29q^{20} - 12q^{21} - 13q^{22} - 20q^{23} - 2q^{24} + 41q^{25} - 20q^{26} - 13q^{27} - 28q^{28} - 35q^{29} - 6q^{30} - 20q^{31} - 25q^{32} - 22q^{33} - q^{34} - 44q^{35} - 28q^{36} - 30q^{37} - 7q^{38} - 8q^{39} + 5q^{40} - 29q^{41} - 104q^{42} - 13q^{43} - 88q^{44} + 63q^{45} + 32q^{46} - 55q^{47} - 14q^{48} - q^{49} + 6q^{50} - 18q^{51} + 3q^{52} - 136q^{53} + 30q^{54} - 100q^{55} + 145q^{56} - 96q^{57} + 17q^{58} - 19q^{59} + 118q^{60} + 42q^{61} + 96q^{62} - 6q^{63} - 124q^{64} - 11q^{65} + 120q^{66} - 26q^{67} + 166q^{68} - 134q^{69} - 7q^{70} - 22q^{71} + 32q^{72} + 8q^{73} - 45q^{74} - 36q^{75} - 41q^{76} + q^{77} - 18q^{78} - 26q^{79} - 440q^{80} + 64q^{81} - 28q^{82} + 61q^{83} - 86q^{84} + 5q^{85} + 15q^{86} + 34q^{87} - q^{88} + 22q^{89} + 96q^{90} - 16q^{91} - 43q^{92} - 110q^{93} - q^{94} - 38q^{95} - 165q^{96} - 14q^{97} - 144q^{98} - 196q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(441, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
441.2.ba.a \(648\) \(3.521\) None \(-5\) \(-10\) \(-9\) \(-7\)