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Properties

Label 1710.2.c
Level $1710$
Weight $2$
Character orbit 1710.c
Rep. character $\chi_{1710}(1709,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $4$
Sturm bound $720$
Trace bound $29$

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Defining parameters

Level: \( N \) \(=\) \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1710.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 285 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(720\)
Trace bound: \(29\)
Distinguishing \(T_p\): \(7\), \(11\), \(29\)

Dimensions

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

Total New Old
Modular forms 376 40 336
Cusp forms 344 40 304
Eisenstein series 32 0 32

Trace form

\( 40 q - 40 q^{4} + O(q^{10}) \) \( 40 q - 40 q^{4} + 40 q^{16} - 32 q^{19} - 32 q^{25} + 8 q^{49} - 24 q^{55} + 96 q^{61} - 40 q^{64} + 32 q^{76} - 88 q^{85} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.c.a 1710.c 285.b $4$ $13.654$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}^{2}q^{2}-q^{4}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{8}+\cdots\)
1710.2.c.b 1710.c 285.b $4$ $13.654$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}^{2}q^{2}-q^{4}+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
1710.2.c.c 1710.c 285.b $8$ $13.654$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{24}q^{2}-q^{4}+(\zeta_{24}^{3}+\zeta_{24}^{4})q^{5}+\cdots\)
1710.2.c.d 1710.c 285.b $24$ $13.654$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(1710, [\chi]) \cong \)