Properties

Label 441.2.bh
Level $441$
Weight $2$
Character orbit 441.bh
Rep. character $\chi_{441}(20,\cdot)$
Character field $\Q(\zeta_{42})$
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.bh (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{42})\)
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

\( 648q - 15q^{2} - 14q^{3} - 57q^{4} - 21q^{5} + 14q^{6} - 5q^{7} - 20q^{9} + O(q^{10}) \) \( 648q - 15q^{2} - 14q^{3} - 57q^{4} - 21q^{5} + 14q^{6} - 5q^{7} - 20q^{9} - 28q^{10} - 15q^{11} + 21q^{12} - 7q^{13} - 114q^{14} - 10q^{15} + 39q^{16} - 18q^{18} - 21q^{20} + 10q^{21} + 3q^{22} + 30q^{23} - 14q^{24} + 41q^{25} + 7q^{27} - 20q^{28} + 75q^{29} - 70q^{30} - 39q^{32} - 14q^{33} - 7q^{34} - 128q^{36} - 10q^{37} + 21q^{38} - 36q^{39} - 7q^{40} - 21q^{41} + 104q^{42} + 3q^{43} - 35q^{45} - 72q^{46} - 147q^{47} - 13q^{49} - 18q^{50} + 22q^{51} - 35q^{52} - 14q^{54} - 112q^{55} - 63q^{56} - 16q^{57} + 33q^{58} - 21q^{59} - 90q^{60} - 56q^{61} - 38q^{63} + 52q^{64} + 27q^{65} - 42q^{66} - 26q^{67} - 182q^{69} - 25q^{70} + 24q^{72} - 28q^{73} + 33q^{74} - 14q^{75} + 21q^{76} + 3q^{77} + 90q^{78} - 2q^{79} + 56q^{81} - 28q^{82} - 21q^{83} + 116q^{84} + 5q^{85} - 123q^{86} - 70q^{87} - 41q^{88} - 224q^{90} - 4q^{91} - 225q^{92} + 112q^{93} - 7q^{94} - 12q^{95} - 371q^{96} + 224q^{99} + O(q^{100}) \)

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.bh.a \(648\) \(3.521\) None \(-15\) \(-14\) \(-21\) \(-5\)