Properties

Label 270.3.h
Level $270$
Weight $3$
Character orbit 270.h
Rep. character $\chi_{270}(71,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $1$
Sturm bound $162$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 270.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(162\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(270, [\chi])\).

Total New Old
Modular forms 240 16 224
Cusp forms 192 16 176
Eisenstein series 48 0 48

Trace form

\( 16 q + 16 q^{4} - 4 q^{7} + O(q^{10}) \) \( 16 q + 16 q^{4} - 4 q^{7} + 20 q^{13} + 36 q^{14} - 32 q^{16} + 80 q^{19} + 24 q^{22} - 108 q^{23} + 40 q^{25} - 16 q^{28} + 72 q^{29} - 16 q^{31} - 48 q^{34} - 88 q^{37} + 72 q^{38} - 108 q^{41} + 92 q^{43} + 24 q^{46} - 216 q^{47} - 84 q^{49} - 40 q^{52} + 72 q^{56} - 144 q^{59} - 76 q^{61} - 128 q^{64} - 180 q^{65} + 56 q^{67} - 72 q^{68} + 60 q^{70} + 416 q^{73} + 288 q^{74} + 80 q^{76} + 684 q^{77} + 80 q^{79} - 192 q^{82} - 396 q^{83} - 60 q^{85} + 216 q^{86} - 48 q^{88} - 656 q^{91} - 216 q^{92} - 84 q^{94} + 360 q^{95} - 16 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(270, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
270.3.h.a 270.h 9.d $16$ $7.357$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{6}q^{2}-2\beta _{10}q^{4}+\beta _{12}q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(270, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(270, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)