Properties

Label 45.8.f
Level $45$
Weight $8$
Character orbit 45.f
Rep. character $\chi_{45}(8,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $28$
Newform subspaces $2$
Sturm bound $48$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 45.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 92 28 64
Cusp forms 76 28 48
Eisenstein series 16 0 16

Trace form

\( 28 q - 2696 q^{7} + 6352 q^{10} - 15908 q^{13} - 75272 q^{16} - 331024 q^{22} + 263536 q^{25} - 1074016 q^{28} + 417968 q^{31} - 80852 q^{37} + 1749288 q^{40} - 1147616 q^{43} + 1162688 q^{46} + 9567928 q^{52}+ \cdots + 68516092 q^{97}+O(q^{100}) \) 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.f.a 45.f 15.e $4$ $14.057$ \(\Q(\zeta_{8})\) None 45.8.f.a \(0\) \(0\) \(0\) \(-3296\) $\mathrm{SU}(2)[C_{4}]$ \(q+2\zeta_{8}q^{2}-124\zeta_{8}^{2}q^{4}+(-275\zeta_{8}+\cdots)q^{5}+\cdots\)
45.8.f.b 45.f 15.e $24$ $14.057$ None 45.8.f.b \(0\) \(0\) \(0\) \(600\) $\mathrm{SU}(2)[C_{4}]$

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

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