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Properties

Label 270.3.l
Level $270$
Weight $3$
Character orbit 270.l
Rep. character $\chi_{270}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $48$
Newform subspaces $2$
Sturm bound $162$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 270.l (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(162\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 480 48 432
Cusp forms 384 48 336
Eisenstein series 96 0 96

Trace form

\( 48 q + O(q^{10}) \) \( 48 q + 24 q^{11} + 96 q^{16} + 72 q^{17} - 24 q^{20} + 120 q^{23} + 12 q^{25} + 576 q^{35} + 168 q^{37} + 72 q^{38} - 48 q^{46} - 12 q^{47} - 96 q^{50} - 768 q^{53} - 264 q^{55} - 48 q^{56} - 48 q^{58} - 96 q^{61} - 288 q^{62} - 408 q^{65} + 156 q^{67} + 72 q^{68} - 48 q^{71} + 96 q^{77} - 96 q^{82} + 624 q^{83} + 96 q^{85} - 432 q^{86} - 336 q^{91} + 240 q^{92} - 696 q^{95} - 396 q^{97} - 288 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.l.a 270.l 45.k $24$ $7.357$ None \(-12\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{12}]$
270.3.l.b 270.l 45.k $24$ $7.357$ None \(12\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{12}]$

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

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