Properties

Label 990.3.e
Level $990$
Weight $3$
Character orbit 990.e
Rep. character $\chi_{990}(89,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $1$
Sturm bound $648$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 990.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(648\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(990, [\chi])\).

Total New Old
Modular forms 448 40 408
Cusp forms 416 40 376
Eisenstein series 32 0 32

Trace form

\( 40 q + 80 q^{4} - 8 q^{10} + 160 q^{16} + 32 q^{19} - 32 q^{25} - 224 q^{31} - 80 q^{34} - 16 q^{40} - 632 q^{49} - 336 q^{61} + 320 q^{64} - 128 q^{70} + 64 q^{76} + 448 q^{79} - 40 q^{85} + 640 q^{91}+ \cdots - 640 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(990, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
990.3.e.a 990.e 15.d $40$ $26.976$ None 990.3.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(990, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(990, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)