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Properties

Label 714.2.i
Level $714$
Weight $2$
Character orbit 714.i
Rep. character $\chi_{714}(205,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $40$
Newform subspaces $15$
Sturm bound $288$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 714.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 15 \)
Sturm bound: \(288\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(714, [\chi])\).

Total New Old
Modular forms 304 40 264
Cusp forms 272 40 232
Eisenstein series 32 0 32

Trace form

\( 40 q - 20 q^{4} + 8 q^{6} - 4 q^{7} - 20 q^{9} + O(q^{10}) \) \( 40 q - 20 q^{4} + 8 q^{6} - 4 q^{7} - 20 q^{9} - 4 q^{10} + 8 q^{11} - 8 q^{14} - 8 q^{15} - 20 q^{16} + 16 q^{19} - 8 q^{21} - 8 q^{22} - 16 q^{23} - 4 q^{24} - 24 q^{25} + 8 q^{26} - 4 q^{28} + 32 q^{29} - 12 q^{31} + 4 q^{33} + 16 q^{34} + 32 q^{35} + 40 q^{36} + 8 q^{37} + 8 q^{38} - 8 q^{39} - 4 q^{40} - 64 q^{41} - 4 q^{42} + 48 q^{43} + 8 q^{44} + 8 q^{46} - 40 q^{47} - 4 q^{49} - 16 q^{50} - 8 q^{53} - 4 q^{54} - 40 q^{55} + 16 q^{56} + 32 q^{57} + 4 q^{58} - 24 q^{59} + 4 q^{60} - 16 q^{61} - 48 q^{62} + 8 q^{63} + 40 q^{64} + 40 q^{65} - 8 q^{67} + 44 q^{70} - 48 q^{71} + 24 q^{74} - 32 q^{76} + 48 q^{77} - 20 q^{79} - 20 q^{81} + 96 q^{83} + 16 q^{84} + 40 q^{86} + 4 q^{87} + 4 q^{88} + 8 q^{89} + 8 q^{90} + 80 q^{91} + 32 q^{92} + 8 q^{94} - 32 q^{95} - 4 q^{96} - 56 q^{97} - 8 q^{98} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(714, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
714.2.i.a 714.i 7.c $2$ $5.701$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.b 714.i 7.c $2$ $5.701$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.c 714.i 7.c $2$ $5.701$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.d 714.i 7.c $2$ $5.701$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.e 714.i 7.c $2$ $5.701$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.f 714.i 7.c $2$ $5.701$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(3\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.g 714.i 7.c $2$ $5.701$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.h 714.i 7.c $2$ $5.701$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.i 714.i 7.c $2$ $5.701$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.j 714.i 7.c $2$ $5.701$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.k 714.i 7.c $2$ $5.701$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.l 714.i 7.c $4$ $5.701$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(-2\) \(-2\) \(-2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
714.2.i.m 714.i 7.c $4$ $5.701$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(-2\) \(-2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
714.2.i.n 714.i 7.c $4$ $5.701$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(-2\) \(2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
714.2.i.o 714.i 7.c $6$ $5.701$ 6.0.11337408.1 None \(3\) \(3\) \(3\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(1-\beta _{2})q^{3}+(-1+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(714, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(714, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 2}\)