Properties

Label 45.8.b
Level $45$
Weight $8$
Character orbit 45.b
Rep. character $\chi_{45}(19,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $4$
Sturm bound $48$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 45.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(48\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(45, [\chi])\).

Total New Old
Modular forms 46 18 28
Cusp forms 38 16 22
Eisenstein series 8 2 6

Trace form

\( 16 q - 924 q^{4} + 294 q^{5} + 464 q^{10} + 2904 q^{11} + 4476 q^{14} + 22676 q^{16} + 19760 q^{19} - 89244 q^{20} + 137116 q^{25} + 574980 q^{26} - 291252 q^{29} - 165520 q^{31} + 412456 q^{34} - 367320 q^{35}+ \cdots + 24745656 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{8}^{\mathrm{new}}(45, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
45.8.b.a 45.b 5.b $2$ $14.057$ \(\Q(\sqrt{-29}) \) None 5.8.b.a \(0\) \(0\) \(-150\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+12q^{4}+(-75-5^{2}\beta )q^{5}+\cdots\)
45.8.b.b 45.b 5.b $2$ $14.057$ \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-15}) \) 45.8.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{2}+123q^{4}+5^{3}\beta q^{5}+251\beta q^{8}+\cdots\)
45.8.b.c 45.b 5.b $4$ $14.057$ \(\Q(\sqrt{-65}, \sqrt{85})\) None 45.8.b.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-132q^{4}+(-2\beta _{1}+\beta _{3})q^{5}+\cdots\)
45.8.b.d 45.b 5.b $8$ $14.057$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 15.8.b.a \(0\) \(0\) \(444\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-83-\beta _{2})q^{4}+(56+4\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(45, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)