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Properties

Label 270.2.r
Level $270$
Weight $2$
Character orbit 270.r
Rep. character $\chi_{270}(23,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $216$
Newform subspaces $1$
Sturm bound $108$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 270.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 \(M_{2}(270, [\chi])\).

Total New Old
Modular forms 696 216 480
Cusp forms 600 216 384
Eisenstein series 96 0 96

Trace form

\( 216 q + 12 q^{6} + O(q^{10}) \) \( 216 q + 12 q^{6} + 24 q^{11} - 24 q^{20} + 24 q^{23} + 36 q^{25} + 12 q^{27} - 72 q^{30} - 12 q^{33} - 108 q^{35} - 12 q^{36} - 36 q^{38} - 72 q^{41} - 48 q^{42} - 60 q^{45} - 48 q^{47} - 12 q^{48} - 48 q^{50} - 192 q^{51} - 12 q^{56} - 36 q^{57} + 36 q^{61} + 84 q^{63} + 24 q^{65} - 72 q^{67} + 36 q^{68} - 48 q^{72} - 36 q^{75} - 240 q^{77} + 24 q^{78} - 24 q^{81} - 60 q^{83} + 72 q^{86} - 252 q^{87} - 48 q^{92} - 96 q^{93} - 60 q^{95} - 72 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(270, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
270.2.r.a 270.r 135.q $216$ $2.156$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{36}]$

Decomposition of \(S_{2}^{\mathrm{old}}(270, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(270, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)