Properties

Label 7.11.d
Level $7$
Weight $11$
Character orbit 7.d
Rep. character $\chi_{7}(3,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $1$
Sturm bound $7$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 7.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(7, [\chi])\).

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

Trace form

\( 12 q - 12 q^{2} - 246 q^{3} - 3700 q^{4} + 3330 q^{5} - 12572 q^{7} - 93504 q^{8} + 182964 q^{9} + O(q^{10}) \) \( 12 q - 12 q^{2} - 246 q^{3} - 3700 q^{4} + 3330 q^{5} - 12572 q^{7} - 93504 q^{8} + 182964 q^{9} - 445740 q^{10} + 82566 q^{11} + 1581468 q^{12} - 934752 q^{14} - 729900 q^{15} - 230152 q^{16} + 389178 q^{17} + 378144 q^{18} - 5517150 q^{19} + 11878986 q^{21} - 19846048 q^{22} - 8131674 q^{23} + 31899384 q^{24} + 6794220 q^{25} + 37885176 q^{26} - 64544228 q^{28} - 86390616 q^{29} + 69082560 q^{30} - 44673798 q^{31} + 82297536 q^{32} + 293090418 q^{33} - 192479070 q^{35} - 895531584 q^{36} + 83071214 q^{37} + 528863040 q^{38} + 45216696 q^{39} + 840782640 q^{40} - 267874488 q^{42} - 975196744 q^{43} - 123891084 q^{44} + 960213420 q^{45} + 348447776 q^{46} + 782650314 q^{47} - 531271524 q^{49} - 3793600080 q^{50} + 90752418 q^{51} + 1019252472 q^{52} + 417566766 q^{53} + 4229214768 q^{54} - 2911004880 q^{56} - 3616618428 q^{57} + 2420166368 q^{58} + 456895242 q^{59} + 1019560500 q^{60} + 1469956122 q^{61} + 962168676 q^{63} - 1697861600 q^{64} - 480821880 q^{65} - 875442996 q^{66} + 1667792862 q^{67} - 3587950548 q^{68} + 4620799680 q^{70} + 9772297272 q^{71} - 5075622576 q^{72} - 3308125038 q^{73} - 8441358900 q^{74} - 13137007020 q^{75} + 1048649574 q^{77} + 25651166688 q^{78} - 2397038922 q^{79} + 1013632920 q^{80} + 394526610 q^{81} - 22926766968 q^{82} + 16162834044 q^{84} + 20859080820 q^{85} - 840264960 q^{86} - 31859197092 q^{87} - 3607027256 q^{88} - 2675986686 q^{89} + 17848798800 q^{91} + 58847183592 q^{92} + 8231670714 q^{93} - 26955870432 q^{94} - 13809374190 q^{95} - 30016813680 q^{96} - 50762451012 q^{98} + 20038367016 q^{99} + O(q^{100}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(7, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
7.11.d.a 7.d 7.d $12$ $4.448$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-12\) \(-246\) \(3330\) \(-12572\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2-\beta _{1}-2\beta _{2})q^{2}+(-3^{3}+2\beta _{1}+\cdots)q^{3}+\cdots\)