Properties

Label 11.12.a
Level $11$
Weight $12$
Character orbit 11.a
Rep. character $\chi_{11}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $12$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 11.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(11))\).

Total New Old
Modular forms 12 8 4
Cusp forms 10 8 2
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
\(+\)\(5\)
\(-\)\(3\)

Trace form

\( 8 q + 32 q^{2} - 233 q^{3} + 9076 q^{4} - 15703 q^{5} + 10942 q^{6} + 73958 q^{7} - 56676 q^{8} + 307703 q^{9} + O(q^{10}) \) \( 8 q + 32 q^{2} - 233 q^{3} + 9076 q^{4} - 15703 q^{5} + 10942 q^{6} + 73958 q^{7} - 56676 q^{8} + 307703 q^{9} + 449510 q^{10} - 322102 q^{11} + 1431584 q^{12} + 1964714 q^{13} + 1988732 q^{14} - 2772689 q^{15} + 3418600 q^{16} + 16395044 q^{17} - 20821822 q^{18} - 19590492 q^{19} + 6760168 q^{20} + 17398534 q^{21} - 5153632 q^{22} - 94440641 q^{23} - 83441748 q^{24} + 44566651 q^{25} - 125238196 q^{26} + 209008465 q^{27} + 200526736 q^{28} - 476100402 q^{29} + 240810694 q^{30} + 371580791 q^{31} + 908210584 q^{32} - 89061203 q^{33} - 1102433800 q^{34} + 254817638 q^{35} - 653073836 q^{36} + 422778399 q^{37} + 534201048 q^{38} + 1255438660 q^{39} - 1542772332 q^{40} + 504799778 q^{41} - 1024191356 q^{42} - 49493922 q^{43} - 541775564 q^{44} - 5756032 q^{45} + 472149670 q^{46} - 4355376128 q^{47} - 3141381208 q^{48} + 2557152516 q^{49} - 4723225718 q^{50} + 8840429458 q^{51} - 1951902872 q^{52} + 4727609532 q^{53} - 5957610494 q^{54} + 176028743 q^{55} + 7812077208 q^{56} + 6252115680 q^{57} + 11275380132 q^{58} + 5320998277 q^{59} - 5610203728 q^{60} - 26469446814 q^{61} + 16803218966 q^{62} - 12584866468 q^{63} + 6698319968 q^{64} + 5207837360 q^{65} + 448688086 q^{66} + 33465935785 q^{67} + 2291826712 q^{68} + 5424714107 q^{69} - 53189453716 q^{70} - 49169436051 q^{71} - 46682928432 q^{72} + 10272916070 q^{73} - 21440089350 q^{74} + 35944240640 q^{75} + 109723150848 q^{76} - 13547932222 q^{77} - 99909542648 q^{78} + 36156478486 q^{79} + 2843409976 q^{80} - 127998534496 q^{81} + 88813826300 q^{82} - 41341594746 q^{83} + 70613000912 q^{84} + 89181763862 q^{85} + 170675303052 q^{86} + 30444967224 q^{87} - 79988878068 q^{88} - 123823053765 q^{89} + 336287620112 q^{90} - 9388521112 q^{91} - 416009937424 q^{92} + 1013667979 q^{93} - 109248658064 q^{94} + 67395785832 q^{95} + 153846148520 q^{96} + 162861068113 q^{97} + 310631219304 q^{98} - 113395848049 q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(11))\) 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
11.12.a.a 11.a 1.a $3$ $8.452$ 3.3.202533.1 None \(0\) \(-393\) \(-7305\) \(-5082\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-131-2\beta _{1}-4\beta _{2})q^{3}+\cdots\)
11.12.a.b 11.a 1.a $5$ $8.452$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(32\) \(160\) \(-8398\) \(79040\) $+$ $\mathrm{SU}(2)$ \(q+(6+\beta _{1})q^{2}+(2^{5}-\beta _{3})q^{3}+(1239+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(11))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(11)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)