Properties

Label 45.3.d
Level $45$
Weight $3$
Character orbit 45.d
Rep. character $\chi_{45}(44,\cdot)$
Character field $\Q$
Dimension $4$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
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 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

Trace form

\( 4 q + 12 q^{4} + O(q^{10}) \) \( 4 q + 12 q^{4} - 28 q^{10} - 76 q^{16} + 80 q^{19} - 44 q^{25} + 104 q^{31} + 112 q^{34} + 28 q^{40} - 56 q^{46} - 308 q^{49} - 72 q^{55} - 88 q^{61} - 116 q^{64} + 504 q^{70} + 240 q^{76} + 56 q^{79} - 112 q^{85} + 504 q^{91} - 224 q^{94} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
45.3.d.a 45.d 15.d $4$ $1.226$ \(\Q(\sqrt{-2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+3q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(45, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)