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Properties

Label 90.11.j
Level $90$
Weight $11$
Character orbit 90.j
Rep. character $\chi_{90}(29,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
Newform subspaces $1$
Sturm bound $198$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 90.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(198\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(90, [\chi])\).

Total New Old
Modular forms 368 120 248
Cusp forms 352 120 232
Eisenstein series 16 0 16

Trace form

\( 120 q - 30720 q^{4} + 9918 q^{5} + 12160 q^{6} - 172900 q^{9} - 653220 q^{11} - 175680 q^{14} + 1781914 q^{15} - 15728640 q^{16} - 5078016 q^{20} - 18127640 q^{21} - 3112960 q^{24} - 9921306 q^{25} - 10065420 q^{29}+ \cdots - 43749358340 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{11}^{\mathrm{new}}(90, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
90.11.j.a 90.j 45.h $120$ $57.182$ None 90.11.j.a \(0\) \(0\) \(9918\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{11}^{\mathrm{old}}(90, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(90, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)