Properties

Label 45.18.f
Level $45$
Weight $18$
Character orbit 45.f
Rep. character $\chi_{45}(8,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $68$
Newform subspaces $1$
Sturm bound $108$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 18 \)
Character orbit: \([\chi]\) \(=\) 45.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(108\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(45, [\chi])\).

Total New Old
Modular forms 212 68 144
Cusp forms 196 68 128
Eisenstein series 16 0 16

Trace form

\( 68 q - 47500168 q^{7} + 2085060752 q^{10} - 1401920236 q^{13} - 373339677832 q^{16} + 614834452528 q^{22} + 2015595550736 q^{25} - 9799700450912 q^{28} - 32762597258192 q^{31} + 110004885161924 q^{37} + 126165920450088 q^{40}+ \cdots + 13\!\cdots\!36 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{18}^{\mathrm{new}}(45, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
45.18.f.a 45.f 15.e $68$ $82.450$ None 45.18.f.a \(0\) \(0\) \(0\) \(-47500168\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{18}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{18}^{\mathrm{old}}(45, [\chi]) \simeq \) \(S_{18}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)