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Properties

Label 45.3.h
Level $45$
Weight $3$
Character orbit 45.h
Rep. character $\chi_{45}(14,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $1$
Sturm bound $18$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 45.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(45, [\chi])\).

Total New Old
Modular forms 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

Trace form

\( 20 q - 18 q^{4} - 12 q^{5} + 12 q^{6} - 18 q^{9} + O(q^{10}) \) \( 20 q - 18 q^{4} - 12 q^{5} + 12 q^{6} - 18 q^{9} + 4 q^{10} - 24 q^{11} + 30 q^{14} + 24 q^{15} - 26 q^{16} - 8 q^{19} + 144 q^{20} - 96 q^{21} - 102 q^{24} + 2 q^{25} - 114 q^{29} - 48 q^{30} + 28 q^{31} - 4 q^{34} + 432 q^{36} + 240 q^{39} - 34 q^{40} + 102 q^{41} - 162 q^{45} + 116 q^{46} - 40 q^{49} - 408 q^{50} - 156 q^{51} - 270 q^{54} + 36 q^{55} - 618 q^{56} + 120 q^{59} + 330 q^{60} - 50 q^{61} + 140 q^{64} + 492 q^{65} - 768 q^{66} + 162 q^{69} - 54 q^{70} + 504 q^{74} + 276 q^{75} - 96 q^{76} - 128 q^{79} + 846 q^{81} + 450 q^{84} - 74 q^{85} + 1488 q^{86} - 990 q^{90} - 288 q^{91} + 218 q^{94} - 762 q^{95} - 474 q^{96} - 468 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(45, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
45.3.h.a 45.h 45.h $20$ $1.226$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 45.3.h.a \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(\beta _{5}-\beta _{6})q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots\)