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Properties

Label 14.4.c
Level $14$
Weight $4$
Character orbit 14.c
Rep. character $\chi_{14}(9,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $4$
Newform subspaces $2$
Sturm bound $8$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 14.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(14, [\chi])\).

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

Trace form

\( 4 q + 6 q^{3} - 8 q^{4} + 2 q^{5} - 16 q^{6} - 48 q^{7} + 28 q^{9} + O(q^{10}) \) \( 4 q + 6 q^{3} - 8 q^{4} + 2 q^{5} - 16 q^{6} - 48 q^{7} + 28 q^{9} + 32 q^{10} + 22 q^{11} + 24 q^{12} - 8 q^{13} + 104 q^{14} + 76 q^{15} - 32 q^{16} - 110 q^{17} - 48 q^{18} - 142 q^{19} - 16 q^{20} - 2 q^{21} - 368 q^{22} - 62 q^{23} + 32 q^{24} + 120 q^{25} + 272 q^{26} + 396 q^{27} + 120 q^{28} + 440 q^{29} - 104 q^{30} - 98 q^{31} - 250 q^{33} - 32 q^{34} - 434 q^{35} - 224 q^{36} + 242 q^{37} + 264 q^{38} - 284 q^{39} + 128 q^{40} - 1080 q^{41} + 240 q^{42} + 272 q^{43} + 88 q^{44} + 164 q^{45} - 152 q^{46} - 30 q^{47} - 192 q^{48} - 188 q^{49} + 128 q^{50} + 314 q^{51} + 16 q^{52} + 810 q^{53} - 184 q^{54} + 1516 q^{55} - 64 q^{56} - 324 q^{57} - 16 q^{58} - 202 q^{59} - 152 q^{60} + 658 q^{61} - 208 q^{62} + 372 q^{63} + 256 q^{64} - 1092 q^{65} - 640 q^{66} - 858 q^{67} - 440 q^{68} - 676 q^{69} - 392 q^{70} - 1760 q^{71} - 192 q^{72} + 18 q^{73} + 528 q^{74} - 296 q^{75} + 1136 q^{76} + 1694 q^{77} + 1664 q^{78} + 34 q^{79} + 32 q^{80} + 22 q^{81} - 912 q^{82} + 688 q^{83} - 632 q^{84} - 92 q^{85} + 768 q^{86} + 676 q^{87} + 736 q^{88} + 1890 q^{89} + 800 q^{90} + 640 q^{91} + 496 q^{92} + 190 q^{93} - 744 q^{94} - 914 q^{95} + 128 q^{96} - 4248 q^{97} - 2640 q^{98} - 1592 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(14, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
14.4.c.a 14.c 7.c $2$ $0.826$ \(\Q(\sqrt{-3}) \) None \(-2\) \(5\) \(9\) \(-28\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}+5\zeta_{6}q^{3}-4\zeta_{6}q^{4}+\cdots\)
14.4.c.b 14.c 7.c $2$ $0.826$ \(\Q(\sqrt{-3}) \) None \(2\) \(1\) \(-7\) \(-20\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}+\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-7+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(14, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)