Properties

Label 810.3.j
Level $810$
Weight $3$
Character orbit 810.j
Rep. character $\chi_{810}(269,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $8$
Sturm bound $486$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 810.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 8 \)
Sturm bound: \(486\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(810, [\chi])\).

Total New Old
Modular forms 696 96 600
Cusp forms 600 96 504
Eisenstein series 96 0 96

Trace form

\( 96 q - 96 q^{4} + O(q^{10}) \) \( 96 q - 96 q^{4} - 192 q^{16} + 12 q^{25} + 120 q^{31} + 48 q^{46} + 288 q^{49} + 384 q^{55} - 96 q^{61} + 768 q^{64} - 240 q^{70} - 624 q^{79} - 24 q^{85} - 336 q^{91} + 168 q^{94} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(810, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
810.3.j.a 810.j 45.h $8$ $22.071$ 8.0.\(\cdots\).3 None 270.3.b.a \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{5})q^{2}-2\beta _{4}q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
810.3.j.b 810.j 45.h $8$ $22.071$ \(\Q(\zeta_{24})\) None 270.3.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{24}-\zeta_{24}^{7})q^{2}+(-2+2\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
810.3.j.c 810.j 45.h $8$ $22.071$ 8.0.\(\cdots\).6 None 30.3.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}-\beta _{6})q^{2}+(-2+2\beta _{1})q^{4}+\cdots\)
810.3.j.d 810.j 45.h $8$ $22.071$ \(\Q(\zeta_{24})\) None 90.3.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{24}-\zeta_{24}^{7})q^{2}+(-2+2\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
810.3.j.e 810.j 45.h $8$ $22.071$ \(\Q(\zeta_{24})\) None 270.3.b.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{24}-\zeta_{24}^{7})q^{2}+(-2+2\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
810.3.j.f 810.j 45.h $8$ $22.071$ 8.0.\(\cdots\).3 None 270.3.b.a \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{5})q^{2}-2\beta _{4}q^{4}+(\beta _{3}+3\beta _{4}+\cdots)q^{5}+\cdots\)
810.3.j.g 810.j 45.h $24$ $22.071$ None 810.3.b.c \(0\) \(0\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{6}]$
810.3.j.h 810.j 45.h $24$ $22.071$ None 810.3.b.c \(0\) \(0\) \(0\) \(24\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(810, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(810, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 2}\)