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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
810.2.e.a \(2\) \(6.468\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-2\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
810.2.e.b \(2\) \(6.468\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(4\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots\)
810.2.e.c \(2\) \(6.468\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-5\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-5+\cdots)q^{7}+\cdots\)
810.2.e.d \(2\) \(6.468\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-2\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
810.2.e.e \(2\) \(6.468\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-2\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
810.2.e.f \(2\) \(6.468\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(1\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
810.2.e.g \(2\) \(6.468\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-5\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-5+\cdots)q^{7}+\cdots\)
810.2.e.h \(2\) \(6.468\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-2\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
810.2.e.i \(2\) \(6.468\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-2\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
810.2.e.j \(2\) \(6.468\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(1\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
810.2.e.k \(2\) \(6.468\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(-2\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
810.2.e.l \(2\) \(6.468\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(4\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+\cdots\)
810.2.e.m \(4\) \(6.468\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(-2\) \(-4\) \(q-\zeta_{12}q^{2}+(-1+\zeta_{12})q^{4}+(-1+\zeta_{12}+\cdots)q^{5}+\cdots\)
810.2.e.n \(4\) \(6.468\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(2\) \(-4\) \(q+\zeta_{12}q^{2}+(-1+\zeta_{12})q^{4}+(1-\zeta_{12}+\cdots)q^{5}+\cdots\)

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

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