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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 37
111.2.a.a \(3\) \(0.886\) 3.3.148.1 None \(3\) \(-3\) \(4\) \(-4\) \(+\) \(-\) \(q+(1+\beta _{2})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
111.2.a.b \(4\) \(0.886\) 4.4.6224.1 None \(0\) \(4\) \(-2\) \(4\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)

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

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