Properties

Label 11.9.b
Level $11$
Weight $9$
Character orbit 11.b
Rep. character $\chi_{11}(10,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $2$
Sturm bound $9$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 11.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(9\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(11, [\chi])\).

Total New Old
Modular forms 9 9 0
Cusp forms 7 7 0
Eisenstein series 2 2 0

Trace form

\( 7 q - 149 q^{3} - 956 q^{4} + 703 q^{5} - 7370 q^{9} + O(q^{10}) \) \( 7 q - 149 q^{3} - 956 q^{4} + 703 q^{5} - 7370 q^{9} - 17677 q^{11} + 25636 q^{12} - 33768 q^{14} - 44239 q^{15} + 377800 q^{16} - 600212 q^{20} - 550440 q^{22} + 151291 q^{23} + 792678 q^{25} - 657432 q^{26} + 1028737 q^{27} - 598549 q^{31} + 1338271 q^{33} - 1345128 q^{34} + 8990608 q^{36} - 3088369 q^{37} - 8900760 q^{38} - 8158920 q^{42} + 17958380 q^{44} + 4645724 q^{45} + 9748006 q^{47} - 26433944 q^{48} - 4301801 q^{49} - 50743394 q^{53} + 24187163 q^{55} + 68829936 q^{56} + 65482560 q^{58} - 33716357 q^{59} + 1773116 q^{60} - 196144304 q^{64} + 75167400 q^{66} + 59226251 q^{67} + 122952077 q^{69} - 168190680 q^{70} + 10262299 q^{71} - 216436164 q^{75} + 91605360 q^{77} + 111889320 q^{78} + 458824888 q^{80} - 149003051 q^{81} - 163977720 q^{82} - 261274512 q^{86} + 328724880 q^{88} - 45315329 q^{89} + 355260528 q^{91} - 592267964 q^{92} - 8413123 q^{93} - 303341329 q^{97} + 250016734 q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(11, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
11.9.b.a 11.b 11.b $1$ $4.481$ \(\Q\) \(\Q(\sqrt{-11}) \) 11.9.b.a \(0\) \(-113\) \(1151\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-113q^{3}+2^{8}q^{4}+1151q^{5}+6208q^{9}+\cdots\)
11.9.b.b 11.b 11.b $6$ $4.481$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None 11.9.b.b \(0\) \(-36\) \(-448\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-6-\beta _{4})q^{3}+(-203+3\beta _{3}+\cdots)q^{4}+\cdots\)