Properties

Label 2014.2.a
Level 2014
Weight 2
Character orbit a
Rep. character \(\chi_{2014}(1,\cdot)\)
Character field \(\Q\)
Dimension 77
Newforms 12
Sturm bound 540
Trace bound 3

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Defining parameters

Level: \( N \) = \( 2014 = 2 \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2014.a (trivial)
Character field: \(\Q\)
Newforms: \( 12 \)
Sturm bound: \(540\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2014))\).

Total New Old
Modular forms 274 77 197
Cusp forms 267 77 190
Eisenstein series 7 0 7

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

\(2\)\(19\)\(53\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(8\)
\(+\)\(+\)\(-\)\(-\)\(11\)
\(+\)\(-\)\(+\)\(-\)\(13\)
\(+\)\(-\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(11\)
\(-\)\(+\)\(-\)\(+\)\(8\)
\(-\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(-\)\(-\)\(12\)
Plus space\(+\)\(30\)
Minus space\(-\)\(47\)

Trace form

\(77q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 89q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(77q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 89q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 8q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 77q^{16} \) \(\mathstrut -\mathstrut 14q^{17} \) \(\mathstrut -\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut q^{19} \) \(\mathstrut +\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 8q^{27} \) \(\mathstrut -\mathstrut 4q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 16q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut -\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 2q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 89q^{36} \) \(\mathstrut -\mathstrut 14q^{37} \) \(\mathstrut -\mathstrut q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut +\mathstrut 8q^{44} \) \(\mathstrut -\mathstrut 38q^{45} \) \(\mathstrut +\mathstrut 16q^{46} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 65q^{49} \) \(\mathstrut -\mathstrut 31q^{50} \) \(\mathstrut +\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 14q^{52} \) \(\mathstrut -\mathstrut q^{53} \) \(\mathstrut -\mathstrut 8q^{54} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 26q^{58} \) \(\mathstrut -\mathstrut 36q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 24q^{62} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 77q^{64} \) \(\mathstrut +\mathstrut 52q^{65} \) \(\mathstrut -\mathstrut 32q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 14q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 16q^{71} \) \(\mathstrut -\mathstrut 13q^{72} \) \(\mathstrut +\mathstrut 26q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut +\mathstrut 28q^{75} \) \(\mathstrut +\mathstrut q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut +\mathstrut 48q^{79} \) \(\mathstrut +\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 69q^{81} \) \(\mathstrut -\mathstrut 26q^{82} \) \(\mathstrut +\mathstrut 76q^{83} \) \(\mathstrut +\mathstrut 24q^{84} \) \(\mathstrut +\mathstrut 52q^{85} \) \(\mathstrut +\mathstrut 4q^{86} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 12q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 14q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut 4q^{92} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 10q^{97} \) \(\mathstrut -\mathstrut 41q^{98} \) \(\mathstrut +\mathstrut 8q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2014))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 19 53
2014.2.a.a \(1\) \(16.082\) \(\Q\) None \(-1\) \(-2\) \(-3\) \(-2\) \(+\) \(-\) \(-\) \(q-q^{2}-2q^{3}+q^{4}-3q^{5}+2q^{6}-2q^{7}+\cdots\)
2014.2.a.b \(1\) \(16.082\) \(\Q\) None \(-1\) \(2\) \(2\) \(3\) \(+\) \(-\) \(+\) \(q-q^{2}+2q^{3}+q^{4}+2q^{5}-2q^{6}+3q^{7}+\cdots\)
2014.2.a.c \(1\) \(16.082\) \(\Q\) None \(1\) \(2\) \(2\) \(-1\) \(-\) \(-\) \(-\) \(q+q^{2}+2q^{3}+q^{4}+2q^{5}+2q^{6}-q^{7}+\cdots\)
2014.2.a.d \(2\) \(16.082\) \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(1+\beta )q^{6}+\cdots\)
2014.2.a.e \(6\) \(16.082\) 6.6.1397493.1 None \(-6\) \(0\) \(-3\) \(6\) \(+\) \(-\) \(-\) \(q-q^{2}+(\beta _{2}+\beta _{3}+\beta _{5})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
2014.2.a.f \(7\) \(16.082\) 7.7.171553549.1 None \(7\) \(-2\) \(-8\) \(-6\) \(-\) \(-\) \(+\) \(q+q^{2}+(-\beta _{1}+\beta _{4})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
2014.2.a.g \(8\) \(16.082\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(0\) \(1\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{5}q^{5}+\beta _{1}q^{6}+\cdots\)
2014.2.a.h \(8\) \(16.082\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(-4\) \(-3\) \(-10\) \(-\) \(+\) \(-\) \(q+q^{2}-\beta _{2}q^{3}+q^{4}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
2014.2.a.i \(9\) \(16.082\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(-2\) \(4\) \(4\) \(-\) \(-\) \(-\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{7}q^{5}-\beta _{1}q^{6}+\cdots\)
2014.2.a.j \(11\) \(16.082\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-11\) \(0\) \(1\) \(-7\) \(+\) \(+\) \(-\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{8}q^{5}+\beta _{1}q^{6}+\cdots\)
2014.2.a.k \(11\) \(16.082\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(11\) \(4\) \(3\) \(7\) \(-\) \(+\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots\)
2014.2.a.l \(12\) \(16.082\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(-4\) \(6\) \(-2\) \(+\) \(-\) \(+\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2014))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2014)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(53))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(106))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1007))\)\(^{\oplus 2}\)