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Properties

Label 1350.3.k
Level $1350$
Weight $3$
Character orbit 1350.k
Rep. character $\chi_{1350}(449,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
Newform subspaces $3$
Sturm bound $810$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1350.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(810\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1350, [\chi])\).

Total New Old
Modular forms 1152 72 1080
Cusp forms 1008 72 936
Eisenstein series 144 0 144

Trace form

\( 72 q - 72 q^{4} + O(q^{10}) \) \( 72 q - 72 q^{4} + 72 q^{11} - 72 q^{14} - 144 q^{16} + 72 q^{29} + 60 q^{31} - 288 q^{41} + 48 q^{46} + 204 q^{49} + 144 q^{56} + 288 q^{59} - 96 q^{61} + 576 q^{64} + 288 q^{74} - 144 q^{79} + 216 q^{86} - 336 q^{91} + 168 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1350, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1350.3.k.a 1350.k 45.h $8$ $36.785$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{24}^{4}+\zeta_{24}^{7})q^{2}-2\zeta_{24}^{2}q^{4}+\cdots\)
1350.3.k.b 1350.k 45.h $32$ $36.785$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
1350.3.k.c 1350.k 45.h $32$ $36.785$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(1350, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1350, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)