Properties

Label 405.2.r
Level $405$
Weight $2$
Character orbit 405.r
Rep. character $\chi_{405}(8,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $192$
Newform subspaces $1$
Sturm bound $108$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
Character field: \(\Q(\zeta_{36})\)
Newform subspaces: \( 1 \)
Sturm bound: \(108\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(405, [\chi])\).

Total New Old
Modular forms 720 240 480
Cusp forms 576 192 384
Eisenstein series 144 48 96

Trace form

\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(405, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
405.2.r.a 405.r 135.q $192$ $3.234$ None 135.2.q.a \(12\) \(0\) \(12\) \(-12\) $\mathrm{SU}(2)[C_{36}]$

Decomposition of \(S_{2}^{\mathrm{old}}(405, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(405, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)