Properties

Label 45.6.j
Level $45$
Weight $6$
Character orbit 45.j
Rep. character $\chi_{45}(4,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $56$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 45.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(45, [\chi])\).

Total New Old
Modular forms 64 64 0
Cusp forms 56 56 0
Eisenstein series 8 8 0

Trace form

\( 56q + 414q^{4} - 30q^{5} + 12q^{6} + 468q^{9} + O(q^{10}) \) \( 56q + 414q^{4} - 30q^{5} + 12q^{6} + 468q^{9} - 68q^{10} - 780q^{11} + 1398q^{14} + 672q^{15} - 5570q^{16} - 8q^{19} + 3522q^{20} - 4848q^{21} - 7554q^{24} - 1654q^{25} + 16968q^{26} + 2700q^{29} + 22578q^{30} - 4436q^{31} - 6268q^{34} - 16344q^{35} + 38016q^{36} + 2508q^{39} + 2036q^{40} - 38928q^{41} - 119400q^{44} - 55890q^{45} + 45764q^{46} + 40244q^{49} - 26466q^{50} - 2964q^{51} + 132894q^{54} + 21024q^{55} - 59442q^{56} + 70200q^{59} + 165084q^{60} + 23368q^{61} - 164668q^{64} - 39210q^{65} + 49452q^{66} - 167076q^{69} + 49752q^{70} + 175176q^{71} + 180168q^{74} - 33528q^{75} - 27348q^{76} - 53480q^{79} + 485892q^{80} - 365112q^{81} - 334242q^{84} + 43936q^{85} - 18060q^{86} - 685536q^{89} - 378936q^{90} - 99576q^{91} + 9614q^{94} - 380028q^{95} - 798q^{96} + 1001340q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(45, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
45.6.j.a \(56\) \(7.217\) None \(0\) \(0\) \(-30\) \(0\)