Properties

Label 14.7.b
Level $14$
Weight $7$
Character orbit 14.b
Rep. character $\chi_{14}(13,\cdot)$
Character field $\Q$
Dimension $4$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
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 14 4 10
Cusp forms 10 4 6
Eisenstein series 4 0 4

Trace form

\( 4 q + 128 q^{4} + 308 q^{7} + 1092 q^{9} + O(q^{10}) \) \( 4 q + 128 q^{4} + 308 q^{7} + 1092 q^{9} - 4440 q^{11} + 2688 q^{14} - 4320 q^{15} + 4096 q^{16} - 9984 q^{18} + 19488 q^{21} + 1536 q^{22} + 40584 q^{23} - 40700 q^{25} + 9856 q^{28} - 18264 q^{29} - 42240 q^{30} - 84000 q^{35} + 34944 q^{36} - 23192 q^{37} + 208608 q^{39} + 80640 q^{42} - 44696 q^{43} - 142080 q^{44} + 33792 q^{46} - 310268 q^{49} + 364800 q^{50} + 157824 q^{51} + 248616 q^{53} + 86016 q^{56} - 472992 q^{57} - 840192 q^{58} - 138240 q^{60} - 125580 q^{63} + 131072 q^{64} + 1293600 q^{65} - 434776 q^{67} + 1102080 q^{70} - 451608 q^{71} - 319488 q^{72} - 981504 q^{74} - 309624 q^{77} + 1301760 q^{78} + 2092904 q^{79} - 252828 q^{81} + 623616 q^{84} - 2117760 q^{85} - 2334720 q^{86} + 49152 q^{88} - 1109472 q^{91} + 1298688 q^{92} + 995328 q^{93} - 190560 q^{95} + 827904 q^{98} - 1331928 q^{99} + O(q^{100}) \)

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.b.a 14.b 7.b $4$ $3.221$ 4.0.211968.1 None \(0\) \(0\) \(0\) \(308\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{1}q^{3}+2^{5}q^{4}-5\beta _{2}q^{5}+\cdots\)

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

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