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Properties

Label 7.11.b
Level $7$
Weight $11$
Character orbit 7.b
Rep. character $\chi_{7}(6,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $2$
Sturm bound $7$
Trace bound $1$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 7 7 0
Cusp forms 5 5 0
Eisenstein series 2 2 0

Trace form

\( 5 q + 9 q^{2} + 1649 q^{4} - 11907 q^{7} + 53865 q^{8} + 30285 q^{9} + O(q^{10}) \) \( 5 q + 9 q^{2} + 1649 q^{4} - 11907 q^{7} + 53865 q^{8} + 30285 q^{9} - 230334 q^{11} - 584031 q^{14} + 529920 q^{15} - 202143 q^{16} + 3446001 q^{18} - 6685910 q^{22} - 7612134 q^{23} + 26129885 q^{25} - 48487607 q^{28} + 35049234 q^{29} - 70744320 q^{30} + 152000409 q^{32} - 151468800 q^{35} + 141885081 q^{36} - 234643806 q^{37} + 489646080 q^{39} - 454406400 q^{42} + 7156866 q^{43} - 1013246022 q^{44} + 1671867106 q^{46} - 708186955 q^{49} + 640508865 q^{50} - 955445760 q^{51} + 1460243394 q^{53} - 1549267839 q^{56} + 803623680 q^{57} - 1248536390 q^{58} + 1468938240 q^{60} - 1066621563 q^{63} + 128609553 q^{64} - 481608960 q^{65} + 46348114 q^{67} + 2877907200 q^{70} - 2474452614 q^{71} + 4380413265 q^{72} - 8199938166 q^{74} + 7241187954 q^{77} - 3893057280 q^{78} + 11109091114 q^{79} - 11928150315 q^{81} + 10905753600 q^{84} - 5489441280 q^{85} + 5913228906 q^{86} - 32859814678 q^{88} + 3483782400 q^{91} + 10053343794 q^{92} + 27132433920 q^{93} - 21990620160 q^{95} + 30109598841 q^{98} - 20410994286 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.b.a 7.b 7.b $1$ $4.448$ \(\Q\) \(\Q(\sqrt{-7}) \) \(57\) \(0\) \(0\) \(-16807\) $\mathrm{U}(1)[D_{2}]$ \(q+57q^{2}+2225q^{4}-7^{5}q^{7}+68457q^{8}+\cdots\)
7.11.b.b 7.b 7.b $4$ $4.448$ 4.0.373770240.2 None \(-48\) \(0\) \(0\) \(4900\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-12+\beta _{2})q^{2}-\beta _{1}q^{3}+(-12^{2}+\cdots)q^{4}+\cdots\)