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Properties

Label 14.7.d
Level $14$
Weight $7$
Character orbit 14.d
Rep. character $\chi_{14}(3,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $1$
Sturm bound $14$
Trace bound $0$

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(14, [\chi])\).

Total New Old
Modular forms 28 8 20
Cusp forms 20 8 12
Eisenstein series 8 0 8

Trace form

\( 8 q - 128 q^{4} - 336 q^{5} + 652 q^{7} + 756 q^{9} + O(q^{10}) \) \( 8 q - 128 q^{4} - 336 q^{5} + 652 q^{7} + 756 q^{9} - 2016 q^{10} - 1356 q^{11} + 2064 q^{14} + 27144 q^{15} - 4096 q^{16} - 17304 q^{17} - 6816 q^{18} - 32004 q^{19} + 9756 q^{21} + 25248 q^{22} - 4128 q^{23} + 10752 q^{24} + 4664 q^{25} - 4704 q^{26} - 7552 q^{28} - 30312 q^{29} + 9648 q^{30} - 3108 q^{31} + 3276 q^{33} + 98028 q^{35} - 48384 q^{36} - 6124 q^{37} + 155568 q^{38} + 100764 q^{39} + 64512 q^{40} - 315936 q^{42} - 297376 q^{43} - 43392 q^{44} - 172116 q^{45} - 194064 q^{46} + 313908 q^{47} + 32432 q^{49} + 38784 q^{50} + 253692 q^{51} + 255360 q^{52} + 278484 q^{53} + 386064 q^{54} - 125952 q^{56} - 81288 q^{57} - 169824 q^{58} - 835464 q^{59} - 434304 q^{60} - 995316 q^{61} + 1216188 q^{63} + 262144 q^{64} + 8316 q^{65} + 1673280 q^{66} + 648808 q^{67} + 553728 q^{68} - 1572816 q^{70} + 190128 q^{71} - 218112 q^{72} - 1617084 q^{73} - 1158144 q^{74} - 2042208 q^{75} + 1456224 q^{77} + 1122432 q^{78} + 70096 q^{79} + 344064 q^{80} + 1177920 q^{81} + 66528 q^{82} - 1133568 q^{84} + 2190984 q^{85} - 573024 q^{86} - 2057076 q^{87} - 403968 q^{88} + 739116 q^{89} + 2233752 q^{91} + 264192 q^{92} - 23364 q^{93} + 3795120 q^{94} + 725640 q^{95} - 344064 q^{96} - 3532320 q^{98} - 4625928 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(14, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
14.7.d.a 14.d 7.d $8$ $3.221$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(-336\) \(652\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}-\beta _{3})q^{2}+(-\beta _{2}+2\beta _{3}-\beta _{6}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

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