Properties

Label 294.4.e
Level $294$
Weight $4$
Character orbit 294.e
Rep. character $\chi_{294}(67,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $40$
Newform subspaces $15$
Sturm bound $224$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 294.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 15 \)
Sturm bound: \(224\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(294, [\chi])\).

Total New Old
Modular forms 368 40 328
Cusp forms 304 40 264
Eisenstein series 64 0 64

Trace form

\( 40q + 6q^{3} - 80q^{4} - 16q^{5} - 24q^{6} - 180q^{9} + O(q^{10}) \) \( 40q + 6q^{3} - 80q^{4} - 16q^{5} - 24q^{6} - 180q^{9} + 52q^{10} + 28q^{11} + 24q^{12} - 12q^{13} - 84q^{15} - 320q^{16} - 260q^{17} + 50q^{19} + 128q^{20} - 568q^{22} + 324q^{23} + 48q^{24} + 10q^{25} + 152q^{26} - 108q^{27} + 40q^{29} - 48q^{30} - 156q^{31} + 138q^{33} - 304q^{34} + 1440q^{36} - 1210q^{37} + 72q^{38} - 294q^{39} + 208q^{40} + 936q^{41} + 1516q^{43} + 112q^{44} - 144q^{45} + 200q^{46} + 72q^{47} - 192q^{48} + 1984q^{50} - 216q^{51} + 24q^{52} - 2396q^{53} + 108q^{54} + 380q^{55} + 300q^{57} - 492q^{58} - 112q^{59} + 168q^{60} + 1764q^{61} + 3536q^{62} + 2560q^{64} + 584q^{65} + 528q^{66} + 2306q^{67} - 1040q^{68} - 1896q^{69} - 4976q^{71} - 746q^{73} + 1720q^{74} + 738q^{75} - 400q^{76} + 1728q^{78} - 584q^{79} - 256q^{80} - 1620q^{81} - 768q^{82} + 3256q^{83} - 1816q^{85} - 40q^{86} - 462q^{87} + 1136q^{88} - 864q^{89} - 936q^{90} - 2592q^{92} + 2346q^{93} + 2160q^{94} - 4264q^{95} + 192q^{96} - 4340q^{97} - 504q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(294, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
294.4.e.a \(2\) \(17.347\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-3\) \(-2\) \(0\) \(q-2\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
294.4.e.b \(2\) \(17.347\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-3\) \(18\) \(0\) \(q-2\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
294.4.e.c \(2\) \(17.347\) \(\Q(\sqrt{-3}) \) None \(-2\) \(3\) \(-18\) \(0\) \(q-2\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
294.4.e.d \(2\) \(17.347\) \(\Q(\sqrt{-3}) \) None \(-2\) \(3\) \(2\) \(0\) \(q-2\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
294.4.e.e \(2\) \(17.347\) \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(-15\) \(0\) \(q+2\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
294.4.e.f \(2\) \(17.347\) \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(-8\) \(0\) \(q+2\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
294.4.e.g \(2\) \(17.347\) \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(6\) \(0\) \(q+2\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
294.4.e.h \(2\) \(17.347\) \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(-6\) \(0\) \(q+2\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
294.4.e.i \(2\) \(17.347\) \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(-6\) \(0\) \(q+2\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
294.4.e.j \(2\) \(17.347\) \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(8\) \(0\) \(q+2\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
294.4.e.k \(4\) \(17.347\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-4\) \(-6\) \(-12\) \(0\) \(q+2\beta _{2}q^{2}+(-3-3\beta _{2})q^{3}+(-4-4\beta _{2}+\cdots)q^{4}+\cdots\)
294.4.e.l \(4\) \(17.347\) \(\Q(\sqrt{-3}, \sqrt{1345})\) None \(-4\) \(6\) \(5\) \(0\) \(q-2\beta _{2}q^{2}+(3-3\beta _{2})q^{3}+(-4+4\beta _{2}+\cdots)q^{4}+\cdots\)
294.4.e.m \(4\) \(17.347\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-4\) \(6\) \(12\) \(0\) \(q+2\beta _{2}q^{2}+(3+3\beta _{2})q^{3}+(-4-4\beta _{2}+\cdots)q^{4}+\cdots\)
294.4.e.n \(4\) \(17.347\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(4\) \(-6\) \(12\) \(0\) \(q+(2+2\beta _{2})q^{2}+3\beta _{2}q^{3}+4\beta _{2}q^{4}+\cdots\)
294.4.e.o \(4\) \(17.347\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(4\) \(6\) \(-12\) \(0\) \(q+(2+2\beta _{2})q^{2}-3\beta _{2}q^{3}+4\beta _{2}q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(294, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(294, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)