Properties

Label 14.5.d
Level $14$
Weight $5$
Character orbit 14.d
Rep. character $\chi_{14}(3,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $10$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 14.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(14, [\chi])\).

Total New Old
Modular forms 20 4 16
Cusp forms 12 4 8
Eisenstein series 8 0 8

Trace form

\( 4 q - 18 q^{3} - 16 q^{4} + 54 q^{5} - 28 q^{7} + 84 q^{9} + O(q^{10}) \) \( 4 q - 18 q^{3} - 16 q^{4} + 54 q^{5} - 28 q^{7} + 84 q^{9} - 96 q^{10} - 54 q^{11} + 144 q^{12} - 708 q^{15} - 128 q^{16} + 918 q^{17} + 576 q^{18} + 30 q^{19} - 378 q^{21} + 192 q^{22} - 486 q^{23} - 768 q^{24} - 572 q^{25} - 1728 q^{26} + 1456 q^{28} + 3240 q^{29} + 1152 q^{30} - 546 q^{31} + 1062 q^{33} - 1890 q^{35} - 1344 q^{36} - 446 q^{37} - 4320 q^{38} - 3312 q^{39} + 768 q^{40} + 5376 q^{42} + 2344 q^{43} - 432 q^{44} + 5724 q^{45} + 3840 q^{46} + 702 q^{47} - 9212 q^{49} - 3456 q^{50} + 318 q^{51} - 384 q^{52} + 2754 q^{53} - 1440 q^{54} - 17460 q^{57} + 384 q^{58} + 12366 q^{59} + 2832 q^{60} + 7686 q^{61} + 6468 q^{63} + 2048 q^{64} - 3024 q^{65} - 3456 q^{66} - 5062 q^{67} - 7344 q^{68} - 2016 q^{70} + 18792 q^{71} + 4608 q^{72} - 17274 q^{73} - 4320 q^{74} - 5220 q^{75} + 4914 q^{77} + 8832 q^{78} + 794 q^{79} - 3456 q^{80} - 4338 q^{81} + 9984 q^{82} - 5040 q^{84} + 10380 q^{85} - 10368 q^{86} - 12276 q^{87} - 768 q^{88} - 12474 q^{89} + 2688 q^{91} + 7776 q^{92} + 18918 q^{93} + 15168 q^{94} + 8910 q^{95} + 6144 q^{96} - 11448 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(14, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
14.5.d.a 14.d 7.d $4$ $1.447$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-18\) \(54\) \(-28\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-6+2\beta _{1}-3\beta _{2}-2\beta _{3})q^{3}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(14, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)