Properties

Label 1710.2.t
Level $1710$
Weight $2$
Character orbit 1710.t
Rep. character $\chi_{1710}(919,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $100$
Newform subspaces $5$
Sturm bound $720$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1710.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(720\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 752 100 652
Cusp forms 688 100 588
Eisenstein series 64 0 64

Trace form

\( 100 q + 50 q^{4} - 2 q^{5} + O(q^{10}) \) \( 100 q + 50 q^{4} - 2 q^{5} - 12 q^{11} + 6 q^{14} - 50 q^{16} + 26 q^{19} - 4 q^{20} - 6 q^{25} + 8 q^{26} + 20 q^{29} + 16 q^{31} - 8 q^{34} - 14 q^{35} + 2 q^{41} - 6 q^{44} + 12 q^{46} - 104 q^{49} - 40 q^{50} - 30 q^{55} + 12 q^{56} + 20 q^{59} + 12 q^{61} - 100 q^{64} - 40 q^{65} - 20 q^{71} - 22 q^{74} + 4 q^{76} + 12 q^{79} - 2 q^{80} + 36 q^{85} + 8 q^{86} + 50 q^{89} + 28 q^{91} + 56 q^{94} + 56 q^{95} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1710.2.t.a 1710.t 95.i $8$ $13.654$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(-1+\zeta_{24}+\cdots)q^{5}+\cdots\)
1710.2.t.b 1710.t 95.i $12$ $13.654$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{2}+\beta _{8}q^{4}+(\beta _{6}-\beta _{11})q^{5}+(3\beta _{4}+\cdots)q^{7}+\cdots\)
1710.2.t.c 1710.t 95.i $20$ $13.654$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{5}q^{2}+\beta _{12}q^{4}+(-\beta _{1}-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots\)
1710.2.t.d 1710.t 95.i $20$ $13.654$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}+\beta _{13})q^{2}+(1-\beta _{3})q^{4}+\beta _{14}q^{5}+\cdots\)
1710.2.t.e 1710.t 95.i $40$ $13.654$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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