Properties

Label 270.2.p
Level $270$
Weight $2$
Character orbit 270.p
Rep. character $\chi_{270}(49,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $108$
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.p (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
Character field: \(\Q(\zeta_{18})\)
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 348 108 240
Cusp forms 300 108 192
Eisenstein series 48 0 48

Trace form

\( 108 q + 6 q^{5} - 6 q^{6} + 12 q^{9} + O(q^{10}) \) \( 108 q + 6 q^{5} - 6 q^{6} + 12 q^{9} - 12 q^{11} + 6 q^{14} + 18 q^{15} + 12 q^{20} - 72 q^{21} - 18 q^{25} - 72 q^{26} + 6 q^{29} + 36 q^{30} + 36 q^{31} + 18 q^{35} - 30 q^{36} - 48 q^{39} - 12 q^{41} - 12 q^{44} - 66 q^{45} + 18 q^{49} - 12 q^{50} + 48 q^{51} - 36 q^{54} - 6 q^{56} - 84 q^{59} + 18 q^{60} - 18 q^{61} + 54 q^{64} - 6 q^{65} - 60 q^{69} - 48 q^{74} + 12 q^{75} - 72 q^{79} - 12 q^{81} - 36 q^{86} - 132 q^{89} + 30 q^{90} - 36 q^{94} - 18 q^{95} - 36 q^{99} + O(q^{100}) \)

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.p.a 270.p 135.p $108$ $2.156$ None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{18}]$

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

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