Properties

Label 1666.2.b
Level $1666$
Weight $2$
Character orbit 1666.b
Rep. character $\chi_{1666}(883,\cdot)$
Character field $\Q$
Dimension $62$
Newform subspaces $15$
Sturm bound $504$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 1666 = 2 \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1666.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(504\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1666, [\chi])\).

Total New Old
Modular forms 268 62 206
Cusp forms 236 62 174
Eisenstein series 32 0 32

Trace form

\( 62 q - 2 q^{2} + 62 q^{4} - 2 q^{8} - 54 q^{9} + O(q^{10}) \) \( 62 q - 2 q^{2} + 62 q^{4} - 2 q^{8} - 54 q^{9} - 24 q^{15} + 62 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 58 q^{25} + 16 q^{26} + 24 q^{30} - 2 q^{32} - 24 q^{33} - 2 q^{34} - 54 q^{36} - 4 q^{38} + 24 q^{43} + 24 q^{47} - 26 q^{50} + 28 q^{53} - 16 q^{55} + 36 q^{59} - 24 q^{60} + 62 q^{64} + 8 q^{66} + 32 q^{67} + 6 q^{68} + 48 q^{69} + 2 q^{72} - 4 q^{76} + 54 q^{81} + 20 q^{83} - 68 q^{85} - 8 q^{86} - 56 q^{87} + 36 q^{89} + 8 q^{93} - 8 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1666, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1666.2.b.a 1666.b 17.b $2$ $13.303$ \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+3iq^{3}+q^{4}-3iq^{6}-q^{8}+\cdots\)
1666.2.b.b 1666.b 17.b $2$ $13.303$ \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+3iq^{3}+q^{4}-3iq^{6}-q^{8}+\cdots\)
1666.2.b.c 1666.b 17.b $2$ $13.303$ \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-q^{8}+\cdots\)
1666.2.b.d 1666.b 17.b $2$ $13.303$ \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}-q^{8}+3q^{9}-2q^{13}+q^{16}+\cdots\)
1666.2.b.e 1666.b 17.b $2$ $13.303$ \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+q^{8}+\cdots\)
1666.2.b.f 1666.b 17.b $2$ $13.303$ \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+q^{8}+\cdots\)
1666.2.b.g 1666.b 17.b $4$ $13.303$ \(\Q(\sqrt{-2}, \sqrt{15})\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{1}q^{5}+\beta _{2}q^{6}+\cdots\)
1666.2.b.h 1666.b 17.b $4$ $13.303$ \(\Q(\sqrt{-2}, \sqrt{15})\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{5}+\beta _{1}q^{6}+\cdots\)
1666.2.b.i 1666.b 17.b $4$ $13.303$ \(\Q(\zeta_{8})\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+q^{4}+(\zeta_{8}+\cdots)q^{6}+\cdots\)
1666.2.b.j 1666.b 17.b $4$ $13.303$ \(\Q(\sqrt{-2}, \sqrt{15})\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
1666.2.b.k 1666.b 17.b $6$ $13.303$ 6.0.84345856.2 None \(6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(\beta _{1}-\beta _{4})q^{3}+q^{4}+(-\beta _{1}-\beta _{5})q^{5}+\cdots\)
1666.2.b.l 1666.b 17.b $6$ $13.303$ 6.0.84345856.2 None \(6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(\beta _{1}-\beta _{4})q^{3}+q^{4}+(-\beta _{1}-\beta _{5})q^{5}+\cdots\)
1666.2.b.m 1666.b 17.b $6$ $13.303$ 6.0.350464.1 None \(6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{2}q^{3}+q^{4}+(\beta _{2}-\beta _{3}+\beta _{5})q^{5}+\cdots\)
1666.2.b.n 1666.b 17.b $8$ $13.303$ 8.0.\(\cdots\).5 None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{3}q^{3}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
1666.2.b.o 1666.b 17.b $8$ $13.303$ 8.0.\(\cdots\).3 None \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-\beta _{6}q^{3}+q^{4}-\beta _{2}q^{5}-\beta _{6}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1666, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1666, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(833, [\chi])\)\(^{\oplus 2}\)