↑

Properties

Label 11.11.b
Level $11$
Weight $11$
Character orbit 11.b
Rep. character $\chi_{11}(10,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $2$
Sturm bound $11$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 11 \)
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: \(11\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 11 11 0
Cusp forms 9 9 0
Eisenstein series 2 2 0

Trace form

\( 9 q + 73 q^{3} - 2844 q^{4} - 571 q^{5} + 170662 q^{9} + O(q^{10}) \) \( 9 q + 73 q^{3} - 2844 q^{4} - 571 q^{5} + 170662 q^{9} - 120923 q^{11} + 373012 q^{12} + 353400 q^{14} - 1026565 q^{15} - 1737816 q^{16} + 4365116 q^{20} + 9315240 q^{22} - 22195447 q^{23} + 9315486 q^{25} + 8548680 q^{26} - 30081221 q^{27} + 92356689 q^{31} + 18130453 q^{33} - 24564840 q^{34} + 50419648 q^{36} - 105432723 q^{37} - 112873560 q^{38} + 68985720 q^{42} - 270124052 q^{44} - 159113716 q^{45} - 590753038 q^{47} + 948403048 q^{48} + 1006497561 q^{49} + 78442058 q^{53} - 865322799 q^{55} + 62137680 q^{56} - 2242105440 q^{58} + 656376521 q^{59} + 663807020 q^{60} + 5476179696 q^{64} - 4481615160 q^{66} - 1465747503 q^{67} - 7062426457 q^{69} + 6517138440 q^{70} - 927946207 q^{71} + 17035999860 q^{75} - 3666944160 q^{77} - 16920303480 q^{78} - 22181640616 q^{80} + 21239333251 q^{81} + 814108680 q^{82} + 47514880080 q^{86} - 21636893520 q^{88} - 20592395923 q^{89} - 34515507360 q^{91} + 36971106452 q^{92} + 1400668511 q^{93} + 64461480957 q^{97} - 61479726770 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
11.11.b.a 11.b 11.b $1$ $6.989$ \(\Q\) \(\Q(\sqrt{-11}) \) \(0\) \(475\) \(-3001\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+475q^{3}+2^{10}q^{4}-3001q^{5}+166576q^{9}+\cdots\)
11.11.b.b 11.b 11.b $8$ $6.989$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-402\) \(2430\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-50+\beta _{2})q^{3}+(-22^{2}+\cdots)q^{4}+\cdots\)