Properties

Label 1710.2.l
Level $1710$
Weight $2$
Character orbit 1710.l
Rep. character $\chi_{1710}(1261,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $72$
Newform subspaces $19$
Sturm bound $720$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1710.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 19 \)
Sturm bound: \(720\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1710, [\chi])\).

Total New Old
Modular forms 752 72 680
Cusp forms 688 72 616
Eisenstein series 64 0 64

Trace form

\( 72q - 2q^{2} - 36q^{4} + 4q^{8} + O(q^{10}) \) \( 72q - 2q^{2} - 36q^{4} + 4q^{8} + 2q^{10} + 4q^{13} + 6q^{14} - 36q^{16} - 12q^{17} + 12q^{19} - 6q^{22} + 4q^{23} - 36q^{25} + 16q^{29} - 16q^{31} - 2q^{32} + 20q^{34} - 2q^{35} + 16q^{37} + 4q^{38} + 2q^{40} - 20q^{41} + 20q^{43} + 12q^{46} - 8q^{47} + 76q^{49} + 4q^{50} + 4q^{52} + 8q^{53} - 12q^{56} + 8q^{58} + 30q^{59} - 24q^{61} + 16q^{62} + 72q^{64} + 8q^{65} - 6q^{67} + 24q^{68} + 4q^{70} + 16q^{71} - 22q^{73} - 34q^{74} + 6q^{76} - 72q^{77} + 36q^{79} - 22q^{82} + 12q^{83} - 16q^{86} + 12q^{88} + 2q^{89} + 28q^{91} + 4q^{92} - 16q^{94} + 4q^{95} - 38q^{97} - 26q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1710, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1710.2.l.a \(2\) \(13.654\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-2\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
1710.2.l.b \(2\) \(13.654\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(4\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
1710.2.l.c \(2\) \(13.654\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-10\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
1710.2.l.d \(2\) \(13.654\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-10\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
1710.2.l.e \(2\) \(13.654\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-10\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
1710.2.l.f \(2\) \(13.654\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-2\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
1710.2.l.g \(2\) \(13.654\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-2\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
1710.2.l.h \(2\) \(13.654\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(2\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
1710.2.l.i \(2\) \(13.654\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(6\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
1710.2.l.j \(4\) \(13.654\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(-2\) \(0\) \(-2\) \(0\) \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
1710.2.l.k \(4\) \(13.654\) \(\Q(\sqrt{-3}, \sqrt{19})\) None \(-2\) \(0\) \(-2\) \(0\) \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
1710.2.l.l \(4\) \(13.654\) \(\Q(\sqrt{-3}, \sqrt{73})\) None \(-2\) \(0\) \(2\) \(-4\) \(q+(-1+\beta _{2})q^{2}-\beta _{2}q^{4}+(1-\beta _{2})q^{5}+\cdots\)
1710.2.l.m \(4\) \(13.654\) \(\Q(\sqrt{-3}, \sqrt{17})\) None \(-2\) \(0\) \(2\) \(10\) \(q-\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+\beta _{2}q^{5}+(2+\cdots)q^{7}+\cdots\)
1710.2.l.n \(4\) \(13.654\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(2\) \(0\) \(2\) \(4\) \(q+(1-\beta _{1})q^{2}-\beta _{1}q^{4}+(1-\beta _{1})q^{5}+\cdots\)
1710.2.l.o \(6\) \(13.654\) 6.0.29654208.1 None \(-3\) \(0\) \(-3\) \(-6\) \(q+(-1+\beta _{1})q^{2}-\beta _{1}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1710.2.l.p \(6\) \(13.654\) 6.0.29654208.1 None \(3\) \(0\) \(3\) \(-6\) \(q+(1-\beta _{1})q^{2}-\beta _{1}q^{4}+(1-\beta _{1})q^{5}+\cdots\)
1710.2.l.q \(6\) \(13.654\) 6.0.29654208.1 None \(3\) \(0\) \(3\) \(2\) \(q+(1-\beta _{1})q^{2}-\beta _{1}q^{4}+(1-\beta _{1})q^{5}+\cdots\)
1710.2.l.r \(8\) \(13.654\) 8.0.4678560000.4 None \(-4\) \(0\) \(4\) \(12\) \(q-\beta _{1}q^{2}+(-1+\beta _{1})q^{4}+\beta _{1}q^{5}+(1+\cdots)q^{7}+\cdots\)
1710.2.l.s \(8\) \(13.654\) 8.0.4678560000.4 None \(4\) \(0\) \(-4\) \(12\) \(q+\beta _{1}q^{2}+(-1+\beta _{1})q^{4}-\beta _{1}q^{5}+(1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1710, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1710, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(855, [\chi])\)\(^{\oplus 2}\)