Properties

Label 1078.2.e
Level $1078$
Weight $2$
Character orbit 1078.e
Rep. character $\chi_{1078}(67,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $64$
Newform subspaces $22$
Sturm bound $336$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 22 \)
Sturm bound: \(336\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(3\), \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1078, [\chi])\).

Total New Old
Modular forms 368 64 304
Cusp forms 304 64 240
Eisenstein series 64 0 64

Trace form

\( 64 q - 32 q^{4} - 4 q^{5} - 8 q^{6} - 24 q^{9} + O(q^{10}) \) \( 64 q - 32 q^{4} - 4 q^{5} - 8 q^{6} - 24 q^{9} - 8 q^{13} + 8 q^{15} - 32 q^{16} + 12 q^{17} - 16 q^{18} + 8 q^{20} - 32 q^{23} + 4 q^{24} - 40 q^{25} - 12 q^{26} + 24 q^{27} + 8 q^{29} - 4 q^{31} - 4 q^{33} + 8 q^{34} + 48 q^{36} + 48 q^{37} - 4 q^{38} + 44 q^{39} + 24 q^{41} - 40 q^{43} + 4 q^{45} - 4 q^{46} + 16 q^{47} - 32 q^{50} - 36 q^{51} + 4 q^{52} - 20 q^{53} + 16 q^{54} - 8 q^{57} + 12 q^{58} - 4 q^{59} - 4 q^{60} + 36 q^{61} - 24 q^{62} + 64 q^{64} + 20 q^{65} - 8 q^{66} + 52 q^{67} + 12 q^{68} - 24 q^{69} + 56 q^{71} - 16 q^{72} - 16 q^{73} + 20 q^{74} - 60 q^{75} + 64 q^{78} + 20 q^{79} - 4 q^{80} - 64 q^{81} - 8 q^{82} - 40 q^{83} - 144 q^{85} - 20 q^{86} + 12 q^{87} - 72 q^{90} + 64 q^{92} + 44 q^{93} - 8 q^{94} - 36 q^{95} + 4 q^{96} + 96 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1078, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1078.2.e.a 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.b 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
1078.2.e.c 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\)
1078.2.e.d 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.e 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(-1\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.f 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.g 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.h 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(1\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.i 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-4\zeta_{6}q^{5}+\cdots\)
1078.2.e.j 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+4\zeta_{6}q^{5}+\cdots\)
1078.2.e.k 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.l 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.m 1078.e 7.c $4$ $8.608$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1078.2.e.n 1078.e 7.c $4$ $8.608$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-2\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1078.2.e.o 1078.e 7.c $4$ $8.608$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+2\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
1078.2.e.p 1078.e 7.c $4$ $8.608$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(-3\beta _{1}+\cdots)q^{5}+\cdots\)
1078.2.e.q 1078.e 7.c $4$ $8.608$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-2\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
1078.2.e.r 1078.e 7.c $4$ $8.608$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}-\beta _{3}q^{6}+\cdots\)
1078.2.e.s 1078.e 7.c $4$ $8.608$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
1078.2.e.t 1078.e 7.c $4$ $8.608$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}-2\beta _{1}q^{5}-q^{8}+\cdots\)
1078.2.e.u 1078.e 7.c $4$ $8.608$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}-\beta _{1}q^{5}-q^{8}+\cdots\)
1078.2.e.v 1078.e 7.c $4$ $8.608$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1078, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1078, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)