Properties

Label 1710.2.d
Level $1710$
Weight $2$
Character orbit 1710.d
Rep. character $\chi_{1710}(1369,\cdot)$
Character field $\Q$
Dimension $46$
Newform subspaces $8$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(720\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\)

Dimensions

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

Total New Old
Modular forms 376 46 330
Cusp forms 344 46 298
Eisenstein series 32 0 32

Trace form

\( 46 q - 46 q^{4} - 6 q^{5} + O(q^{10}) \) \( 46 q - 46 q^{4} - 6 q^{5} + 4 q^{10} + 8 q^{11} - 4 q^{14} + 46 q^{16} - 2 q^{19} + 6 q^{20} - 18 q^{25} - 20 q^{26} + 4 q^{29} + 16 q^{31} - 20 q^{35} - 4 q^{40} + 12 q^{41} - 8 q^{44} - 4 q^{46} - 46 q^{49} + 8 q^{50} - 8 q^{55} + 4 q^{56} + 24 q^{59} + 4 q^{61} - 46 q^{64} - 44 q^{65} + 16 q^{70} + 32 q^{71} + 12 q^{74} + 2 q^{76} + 24 q^{79} - 6 q^{80} + 4 q^{85} + 20 q^{86} + 20 q^{89} - 64 q^{91} + 12 q^{94} - 2 q^{95} + O(q^{100}) \)

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.d.a $2$ $13.654$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{2}-q^{4}+(-2+i)q^{5}-iq^{8}+\cdots\)
1710.2.d.b $2$ $13.654$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q-iq^{2}-q^{4}+(1+2i)q^{5}+iq^{8}+(2+\cdots)q^{10}+\cdots\)
1710.2.d.c $4$ $13.654$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{2}-q^{4}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\)
1710.2.d.d $6$ $13.654$ 6.0.5161984.1 None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{4}q^{2}-q^{4}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
1710.2.d.e $6$ $13.654$ 6.0.350464.1 None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{2}-\beta _{5})q^{7}+\cdots\)
1710.2.d.f $6$ $13.654$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{4}-\beta _{4}q^{5}+(-\beta _{2}-\beta _{5})q^{7}+\cdots\)
1710.2.d.g $8$ $13.654$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}q^{2}-q^{4}+\zeta_{24}^{7}q^{5}+(\zeta_{24}^{2}+\cdots)q^{7}+\cdots\)
1710.2.d.h $12$ $13.654$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}-q^{4}-\beta _{2}q^{5}-\beta _{1}q^{7}+\beta _{3}q^{8}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1710, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(855, [\chi])\)\(^{\oplus 2}\)