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Properties

Label 111.2.a
Level $111$
Weight $2$
Character orbit 111.a
Rep. character $\chi_{111}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $2$
Sturm bound $25$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 111 = 3 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 111.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(25\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(111))\).

Total New Old
Modular forms 14 7 7
Cusp forms 11 7 4
Eisenstein series 3 0 3

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

\(3\)\(37\)FrickeDim
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(4\)
Plus space\(+\)\(0\)
Minus space\(-\)\(7\)

Trace form

\( 7 q + 3 q^{2} + q^{3} + 9 q^{4} + 2 q^{5} - 3 q^{6} + 3 q^{8} + 7 q^{9} + O(q^{10}) \) \( 7 q + 3 q^{2} + q^{3} + 9 q^{4} + 2 q^{5} - 3 q^{6} + 3 q^{8} + 7 q^{9} - 10 q^{10} + 4 q^{11} - q^{12} + 2 q^{13} - 12 q^{14} - 6 q^{15} + q^{16} + 2 q^{17} + 3 q^{18} - 22 q^{20} + 8 q^{21} - 20 q^{22} - 12 q^{23} - 15 q^{24} + 9 q^{25} - 22 q^{26} + q^{27} - 24 q^{28} + 14 q^{29} + 2 q^{30} - 4 q^{31} - q^{32} - 4 q^{33} + 10 q^{34} - 4 q^{35} + 9 q^{36} - q^{37} + 8 q^{38} + 6 q^{39} - 10 q^{40} + 30 q^{41} + 4 q^{42} - 8 q^{43} + 36 q^{44} + 2 q^{45} + 16 q^{46} - 16 q^{47} - 9 q^{48} + 31 q^{49} + 25 q^{50} - 6 q^{51} - 18 q^{52} + 2 q^{53} - 3 q^{54} - 8 q^{55} - 32 q^{56} + 16 q^{57} + 38 q^{58} - 4 q^{59} + 2 q^{60} - 14 q^{61} + 4 q^{62} + 33 q^{64} + 36 q^{65} - 4 q^{66} - 20 q^{67} + 50 q^{68} - 8 q^{69} + 8 q^{70} + 3 q^{72} + 6 q^{73} + 3 q^{74} - 9 q^{75} + 32 q^{76} - 32 q^{77} + 6 q^{78} + 4 q^{79} - 38 q^{80} + 7 q^{81} - 10 q^{82} - 20 q^{83} + 24 q^{84} - 12 q^{85} + 24 q^{86} - 18 q^{87} + 4 q^{88} + 22 q^{89} - 10 q^{90} - 40 q^{91} - 40 q^{92} + 12 q^{93} + 24 q^{94} - 56 q^{95} - 23 q^{96} - 18 q^{97} + 75 q^{98} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(111))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 37
111.2.a.a 111.a 1.a $3$ $0.886$ 3.3.148.1 None 111.2.a.a \(3\) \(-3\) \(4\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
111.2.a.b 111.a 1.a $4$ $0.886$ 4.4.6224.1 None 111.2.a.b \(0\) \(4\) \(-2\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(111))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(111)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 2}\)