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Properties

Label 810.3.h
Level $810$
Weight $3$
Character orbit 810.h
Rep. character $\chi_{810}(431,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $5$
Sturm bound $486$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 810.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(486\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 696 64 632
Cusp forms 600 64 536
Eisenstein series 96 0 96

Trace form

\( 64 q + 64 q^{4} + 20 q^{7} + O(q^{10}) \) \( 64 q + 64 q^{4} + 20 q^{7} - 100 q^{13} - 128 q^{16} - 328 q^{19} - 48 q^{22} + 160 q^{25} + 80 q^{28} + 80 q^{31} + 96 q^{34} + 440 q^{37} - 280 q^{43} - 48 q^{46} - 12 q^{49} + 200 q^{52} + 92 q^{61} - 512 q^{64} + 188 q^{67} - 120 q^{70} + 8 q^{73} - 328 q^{76} - 364 q^{79} + 384 q^{82} + 120 q^{85} + 96 q^{88} - 392 q^{91} + 168 q^{94} + 260 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
810.3.h.a 810.h 9.d $8$ $22.071$ 8.0.3317760000.8 None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{3}-\beta _{4})q^{2}+(2-2\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)
810.3.h.b 810.h 9.d $8$ $22.071$ 8.0.3317760000.8 None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{3}-\beta _{4})q^{2}+(2-2\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)
810.3.h.c 810.h 9.d $16$ $22.071$ 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{13}q^{2}+(2-2\beta _{2})q^{4}+(\beta _{1}+\beta _{9}+\cdots)q^{5}+\cdots\)
810.3.h.d 810.h 9.d $16$ $22.071$ 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{9}q^{2}+2\beta _{4}q^{4}+\beta _{1}q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots\)
810.3.h.e 810.h 9.d $16$ $22.071$ 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{13}q^{2}+(2-2\beta _{2})q^{4}+(-\beta _{1}-\beta _{9}+\cdots)q^{5}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(810, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 2}\)