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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1078.2.e.a \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-2\) \(-2\) \(0\) \(q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.b \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(0\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
1078.2.e.c \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(0\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\)
1078.2.e.d \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(0\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.e \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(-1\) \(2\) \(2\) \(0\) \(q-\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.f \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(2\) \(0\) \(q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.g \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(-4\) \(0\) \(q+\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.h \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(1\) \(-2\) \(-2\) \(0\) \(q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.i \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-4\) \(0\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-4\zeta_{6}q^{5}+\cdots\)
1078.2.e.j \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(4\) \(0\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+4\zeta_{6}q^{5}+\cdots\)
1078.2.e.k \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(0\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.l \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(2\) \(0\) \(q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.m \(4\) \(8.608\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(-2\) \(-4\) \(0\) \(q+\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1078.2.e.n \(4\) \(8.608\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-2\) \(-2\) \(2\) \(0\) \(q+\beta _{1}q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1078.2.e.o \(4\) \(8.608\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+2\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
1078.2.e.p \(4\) \(8.608\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(-3\beta _{1}+\cdots)q^{5}+\cdots\)
1078.2.e.q \(4\) \(8.608\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-2\) \(2\) \(-2\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
1078.2.e.r \(4\) \(8.608\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}-\beta _{3}q^{6}+\cdots\)
1078.2.e.s \(4\) \(8.608\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
1078.2.e.t \(4\) \(8.608\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(0\) \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}-2\beta _{1}q^{5}-q^{8}+\cdots\)
1078.2.e.u \(4\) \(8.608\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(0\) \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}-\beta _{1}q^{5}-q^{8}+\cdots\)
1078.2.e.v \(4\) \(8.608\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(0\) \(2\) \(0\) \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)

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

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