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Properties

Label 11.10.a
Level $11$
Weight $10$
Character orbit 11.a
Rep. character $\chi_{11}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $10$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 11.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(10\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(11))\).

Total New Old
Modular forms 10 8 2
Cusp forms 8 8 0
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(11\)Dim
\(+\)\(3\)
\(-\)\(5\)

Trace form

\( 8 q + 16 q^{2} - 74 q^{3} + 1620 q^{4} - 230 q^{5} - 578 q^{6} + 1140 q^{7} + 20652 q^{8} + 89342 q^{9} + O(q^{10}) \) \( 8 q + 16 q^{2} - 74 q^{3} + 1620 q^{4} - 230 q^{5} - 578 q^{6} + 1140 q^{7} + 20652 q^{8} + 89342 q^{9} - 83738 q^{10} + 29282 q^{11} + 39248 q^{12} - 46044 q^{13} + 24412 q^{14} - 19106 q^{15} - 432120 q^{16} - 528560 q^{17} + 1174610 q^{18} - 1190296 q^{19} - 2069896 q^{20} - 462428 q^{21} + 234256 q^{22} + 5090582 q^{23} + 488700 q^{24} + 4604214 q^{25} + 3194668 q^{26} - 5045294 q^{27} - 5047520 q^{28} + 3174756 q^{29} + 4505830 q^{30} + 7205094 q^{31} - 18294040 q^{32} + 4363018 q^{33} - 5679944 q^{34} - 14501708 q^{35} - 5775164 q^{36} - 1798954 q^{37} + 1039992 q^{38} + 54037792 q^{39} - 27552684 q^{40} - 4175684 q^{41} - 73685276 q^{42} + 47957684 q^{43} - 2986764 q^{44} - 23906560 q^{45} - 21202042 q^{46} + 2547848 q^{47} + 173389640 q^{48} + 52376928 q^{49} + 188003306 q^{50} - 197964644 q^{51} + 98761240 q^{52} - 41405544 q^{53} - 248932046 q^{54} + 50042938 q^{55} + 35350008 q^{56} - 300438024 q^{57} - 57004092 q^{58} + 345886082 q^{59} + 81928544 q^{60} + 225292700 q^{61} - 248605562 q^{62} - 117057784 q^{63} - 467302720 q^{64} - 496809896 q^{65} + 312351094 q^{66} + 653677834 q^{67} - 1061562904 q^{68} - 165010498 q^{69} + 1585529068 q^{70} - 48179694 q^{71} + 1470546336 q^{72} - 299529612 q^{73} - 452221206 q^{74} - 1525780696 q^{75} - 841669744 q^{76} + 229278060 q^{77} + 2174191720 q^{78} - 1467250820 q^{79} + 17771864 q^{80} + 3123036200 q^{81} + 289855036 q^{82} + 1618138740 q^{83} - 3190963840 q^{84} + 827755396 q^{85} - 1505983188 q^{86} - 2316789168 q^{87} + 889879980 q^{88} + 152250798 q^{89} - 7038414304 q^{90} - 1260663328 q^{91} + 5457058144 q^{92} + 1764718990 q^{93} + 5948451440 q^{94} - 2704939944 q^{95} + 1363238456 q^{96} - 2447938502 q^{97} - 3560544360 q^{98} + 881915276 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(11))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 11
11.10.a.a 11.a 1.a $3$ $5.665$ 3.3.2659452.1 None \(0\) \(-186\) \(-1824\) \(-7260\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-62+4\beta _{1}-\beta _{2})q^{3}+(304+\cdots)q^{4}+\cdots\)
11.10.a.b 11.a 1.a $5$ $5.665$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(16\) \(112\) \(1594\) \(8400\) $-$ $\mathrm{SU}(2)$ \(q+(3+\beta _{1})q^{2}+(22+3\beta _{1}+\beta _{4})q^{3}+\cdots\)