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Properties

Label 270.4.i
Level $270$
Weight $4$
Character orbit 270.i
Rep. character $\chi_{270}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $36$
Newform subspaces $1$
Sturm bound $216$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 270.i (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 \(M_{4}(270, [\chi])\).

Total New Old
Modular forms 348 36 312
Cusp forms 300 36 264
Eisenstein series 48 0 48

Trace form

\( 36 q + 72 q^{4} + 8 q^{5} + O(q^{10}) \) \( 36 q + 72 q^{4} + 8 q^{5} + 52 q^{11} - 68 q^{14} - 288 q^{16} - 32 q^{20} - 144 q^{25} - 624 q^{26} - 750 q^{29} + 72 q^{31} - 572 q^{35} + 706 q^{41} + 416 q^{44} + 504 q^{46} + 1080 q^{49} + 488 q^{50} - 180 q^{55} + 272 q^{56} - 2000 q^{59} + 18 q^{61} - 2304 q^{64} + 126 q^{65} - 36 q^{70} - 5592 q^{71} - 1784 q^{74} + 684 q^{79} - 256 q^{80} + 828 q^{85} + 1976 q^{86} + 9284 q^{89} + 1008 q^{91} - 612 q^{94} - 2772 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(270, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
270.4.i.a 270.i 45.j $36$ $15.931$ None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(270, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(270, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)