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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
45.6.j.a 45.j 45.j $56$ $7.217$ None \(0\) \(0\) \(-30\) \(0\) $\mathrm{SU}(2)[C_{6}]$