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Properties

Label 405.3.s
Level $405$
Weight $3$
Character orbit 405.s
Rep. character $\chi_{405}(37,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $408$
Newform subspaces $1$
Sturm bound $162$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 405.s (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
Character field: \(\Q(\zeta_{36})\)
Newform subspaces: \( 1 \)
Sturm bound: \(162\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(405, [\chi])\).

Total New Old
Modular forms 1368 456 912
Cusp forms 1224 408 816
Eisenstein series 144 48 96

Trace form

\( 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8} + O(q^{10}) \) \( 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8} - 6 q^{10} + 60 q^{11} - 12 q^{13} - 24 q^{16} + 6 q^{17} + 300 q^{20} - 12 q^{22} + 156 q^{23} + 6 q^{25} + 48 q^{26} - 24 q^{28} - 24 q^{31} - 72 q^{32} - 156 q^{35} - 6 q^{37} + 252 q^{38} - 108 q^{40} + 384 q^{41} - 12 q^{43} - 12 q^{46} + 210 q^{47} - 276 q^{50} - 60 q^{52} - 516 q^{53} - 24 q^{55} - 912 q^{56} - 12 q^{58} - 312 q^{61} + 6 q^{62} - 420 q^{65} - 480 q^{67} + 540 q^{68} - 12 q^{70} + 12 q^{71} - 6 q^{73} - 216 q^{76} + 876 q^{77} + 1644 q^{80} - 24 q^{82} + 372 q^{83} - 12 q^{85} - 516 q^{86} + 348 q^{88} - 12 q^{91} - 2082 q^{92} - 198 q^{95} + 600 q^{97} + 1032 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(405, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
405.3.s.a 405.s 135.r $408$ $11.035$ None \(12\) \(0\) \(12\) \(-12\) $\mathrm{SU}(2)[C_{36}]$

Decomposition of \(S_{3}^{\mathrm{old}}(405, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(405, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)