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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
294.4.e.a 294.e 7.c $2$ $17.347$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-3\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
294.4.e.b 294.e 7.c $2$ $17.347$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-3\) \(18\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
294.4.e.c 294.e 7.c $2$ $17.347$ \(\Q(\sqrt{-3}) \) None \(-2\) \(3\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
294.4.e.d 294.e 7.c $2$ $17.347$ \(\Q(\sqrt{-3}) \) None \(-2\) \(3\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
294.4.e.e 294.e 7.c $2$ $17.347$ \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(-15\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
294.4.e.f 294.e 7.c $2$ $17.347$ \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
294.4.e.g 294.e 7.c $2$ $17.347$ \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
294.4.e.h 294.e 7.c $2$ $17.347$ \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
294.4.e.i 294.e 7.c $2$ $17.347$ \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
294.4.e.j 294.e 7.c $2$ $17.347$ \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(8\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
294.4.e.k 294.e 7.c $4$ $17.347$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-4\) \(-6\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{2}q^{2}+(-3-3\beta _{2})q^{3}+(-4-4\beta _{2}+\cdots)q^{4}+\cdots\)
294.4.e.l 294.e 7.c $4$ $17.347$ \(\Q(\sqrt{-3}, \sqrt{1345})\) None \(-4\) \(6\) \(5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{2}q^{2}+(3-3\beta _{2})q^{3}+(-4+4\beta _{2}+\cdots)q^{4}+\cdots\)
294.4.e.m 294.e 7.c $4$ $17.347$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-4\) \(6\) \(12\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{2}q^{2}+(3+3\beta _{2})q^{3}+(-4-4\beta _{2}+\cdots)q^{4}+\cdots\)
294.4.e.n 294.e 7.c $4$ $17.347$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(4\) \(-6\) \(12\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2+2\beta _{2})q^{2}+3\beta _{2}q^{3}+4\beta _{2}q^{4}+\cdots\)
294.4.e.o 294.e 7.c $4$ $17.347$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(4\) \(6\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2+2\beta _{2})q^{2}-3\beta _{2}q^{3}+4\beta _{2}q^{4}+\cdots\)

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

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