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Properties

Label 360.3.bn
Level $360$
Weight $3$
Character orbit 360.bn
Rep. character $\chi_{360}(209,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
Newform subspaces $1$
Sturm bound $216$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 360.bn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(216\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(360, [\chi])\).

Total New Old
Modular forms 304 72 232
Cusp forms 272 72 200
Eisenstein series 32 0 32

Trace form

\( 72 q - 8 q^{9} + O(q^{10}) \) \( 72 q - 8 q^{9} - 40 q^{15} - 4 q^{21} + 108 q^{29} - 16 q^{39} + 72 q^{41} - 76 q^{45} + 228 q^{49} + 24 q^{51} + 24 q^{55} + 216 q^{59} - 48 q^{61} - 172 q^{69} - 52 q^{75} - 120 q^{79} - 340 q^{81} - 48 q^{85} + 468 q^{95} - 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(360, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
360.3.bn.a 360.bn 45.h $72$ $9.809$ None 360.3.bn.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(360, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(360, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)