Properties

Label 270.3.j
Level $270$
Weight $3$
Character orbit 270.j
Rep. character $\chi_{270}(89,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
Newform subspaces $2$
Sturm bound $162$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 270.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(162\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 240 24 216
Cusp forms 192 24 168
Eisenstein series 48 0 48

Trace form

\( 24 q - 24 q^{4} - 18 q^{5} + O(q^{10}) \) \( 24 q - 24 q^{4} - 18 q^{5} - 36 q^{11} + 36 q^{14} - 48 q^{16} + 36 q^{20} - 6 q^{25} - 36 q^{29} - 60 q^{31} + 144 q^{41} - 24 q^{46} + 108 q^{49} - 288 q^{50} - 156 q^{55} - 72 q^{56} + 36 q^{59} + 48 q^{61} + 192 q^{64} + 414 q^{65} + 48 q^{70} - 144 q^{74} + 132 q^{79} + 48 q^{85} + 432 q^{86} + 168 q^{91} - 84 q^{94} - 540 q^{95} + O(q^{100}) \)

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.j.a 270.j 45.h $8$ $7.357$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{24}^{4}+\zeta_{24}^{7})q^{2}-2\zeta_{24}^{2}q^{4}+\cdots\)
270.3.j.b 270.j 45.h $16$ $7.357$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-30\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-2-2\beta _{2})q^{4}+(\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)

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

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