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Properties

Label 14.9.d
Level $14$
Weight $9$
Character orbit 14.d
Rep. character $\chi_{14}(3,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $1$
Sturm bound $18$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
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: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(14, [\chi])\).

Total New Old
Modular forms 36 12 24
Cusp forms 28 12 16
Eisenstein series 8 0 8

Trace form

\( 12 q + 162 q^{3} - 768 q^{4} + 1674 q^{5} - 1308 q^{7} + 23604 q^{9} + O(q^{10}) \) \( 12 q + 162 q^{3} - 768 q^{4} + 1674 q^{5} - 1308 q^{7} + 23604 q^{9} + 17664 q^{10} + 10302 q^{11} - 20736 q^{12} + 56832 q^{14} - 255468 q^{15} - 98304 q^{16} + 173178 q^{17} + 16896 q^{18} + 405978 q^{19} - 656910 q^{21} - 941568 q^{22} + 158934 q^{23} + 98304 q^{24} + 838668 q^{25} + 1958400 q^{26} - 255744 q^{28} - 4355256 q^{29} + 916992 q^{30} + 4520250 q^{31} + 4954482 q^{33} - 5270790 q^{35} - 6042624 q^{36} + 134214 q^{37} + 1278720 q^{38} + 1335384 q^{39} - 2260992 q^{40} + 6660096 q^{42} - 12961896 q^{43} + 1318656 q^{44} - 8415396 q^{45} + 2345472 q^{46} + 18385002 q^{47} - 3659172 q^{49} + 2970624 q^{50} - 2673894 q^{51} - 3369984 q^{52} - 16540506 q^{53} - 19646208 q^{54} + 4325376 q^{56} + 100263780 q^{57} + 9176064 q^{58} + 31163922 q^{59} + 16349952 q^{60} - 85390158 q^{61} + 4361988 q^{63} + 25165824 q^{64} - 46506264 q^{65} - 111873024 q^{66} - 37750362 q^{67} - 22166784 q^{68} + 92031744 q^{70} + 45506424 q^{71} + 2162688 q^{72} + 9414786 q^{73} + 58837248 q^{74} + 9837540 q^{75} - 100614066 q^{77} - 25463808 q^{78} + 59730294 q^{79} - 27426816 q^{80} - 89677422 q^{81} - 93259776 q^{82} + 122616576 q^{84} - 64652220 q^{85} - 15144960 q^{86} + 334229724 q^{87} + 60260352 q^{88} + 323014482 q^{89} - 266861424 q^{91} - 40687104 q^{92} - 11119662 q^{93} - 443440128 q^{94} - 175918350 q^{95} - 12582912 q^{96} + 472166400 q^{98} - 346906296 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(14, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
14.9.d.a 14.d 7.d $12$ $5.703$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(162\) \(1674\) \(-1308\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}+\beta _{3})q^{2}+(18-9\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(14, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)