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Properties

Label 810.2.e
Level $810$
Weight $2$
Character orbit 810.e
Rep. character $\chi_{810}(271,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $32$
Newform subspaces $14$
Sturm bound $324$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 810.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 14 \)
Sturm bound: \(324\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(810, [\chi])\).

Total New Old
Modular forms 372 32 340
Cusp forms 276 32 244
Eisenstein series 96 0 96

Trace form

\( 32 q - 16 q^{4} - 20 q^{7} + O(q^{10}) \) \( 32 q - 16 q^{4} - 20 q^{7} - 20 q^{13} - 16 q^{16} + 16 q^{19} + 12 q^{22} - 16 q^{25} + 40 q^{28} - 20 q^{31} + 12 q^{34} + 40 q^{37} - 8 q^{43} - 24 q^{46} - 24 q^{49} - 20 q^{52} + 16 q^{61} + 32 q^{64} + 16 q^{67} + 12 q^{70} - 32 q^{73} - 8 q^{76} + 4 q^{79} - 24 q^{82} + 24 q^{85} + 12 q^{88} - 16 q^{91} + 12 q^{94} - 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(810, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
810.2.e.a 810.e 9.c $2$ $6.468$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
810.2.e.b 810.e 9.c $2$ $6.468$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots\)
810.2.e.c 810.e 9.c $2$ $6.468$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-5+\cdots)q^{7}+\cdots\)
810.2.e.d 810.e 9.c $2$ $6.468$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
810.2.e.e 810.e 9.c $2$ $6.468$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
810.2.e.f 810.e 9.c $2$ $6.468$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
810.2.e.g 810.e 9.c $2$ $6.468$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-5+\cdots)q^{7}+\cdots\)
810.2.e.h 810.e 9.c $2$ $6.468$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
810.2.e.i 810.e 9.c $2$ $6.468$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
810.2.e.j 810.e 9.c $2$ $6.468$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
810.2.e.k 810.e 9.c $2$ $6.468$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
810.2.e.l 810.e 9.c $2$ $6.468$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+\cdots\)
810.2.e.m 810.e 9.c $4$ $6.468$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}q^{2}+(-1+\zeta_{12})q^{4}+(-1+\zeta_{12}+\cdots)q^{5}+\cdots\)
810.2.e.n 810.e 9.c $4$ $6.468$ \(\Q(\zeta_{12})\) None \(2\) \(0\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{12}q^{2}+(-1+\zeta_{12})q^{4}+(1-\zeta_{12}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(810, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(810, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 2}\)