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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

\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} + O(q^{10}) \) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM 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 \(12\) \(0\) \(12\) \(-12\) $\mathrm{SU}(2)[C_{36}]$

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

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