↑

Properties

Label 6026.2.a
Level 6026
Weight 2
Character orbit a
Rep. character \(\chi_{6026}(1,\cdot)\)
Character field \(\Q\)
Dimension 241
Newforms 13
Sturm bound 1584
Trace bound 5

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)
Character field: \(\Q\)
Newforms: \( 13 \)
Sturm bound: \(1584\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6026))\).

Total New Old
Modular forms 796 241 555
Cusp forms 789 241 548
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.

\(2\)\(23\)\(131\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(25\)
\(+\)\(+\)\(-\)\(-\)\(36\)
\(+\)\(-\)\(+\)\(-\)\(34\)
\(+\)\(-\)\(-\)\(+\)\(25\)
\(-\)\(+\)\(+\)\(-\)\(37\)
\(-\)\(+\)\(-\)\(+\)\(23\)
\(-\)\(-\)\(+\)\(+\)\(20\)
\(-\)\(-\)\(-\)\(-\)\(41\)
Plus space\(+\)\(93\)
Minus space\(-\)\(148\)

Trace form

\( 241q + q^{2} + 241q^{4} - 2q^{5} - 4q^{6} + 8q^{7} + q^{8} + 257q^{9} + O(q^{10}) \) \( 241q + q^{2} + 241q^{4} - 2q^{5} - 4q^{6} + 8q^{7} + q^{8} + 257q^{9} + 6q^{10} + 4q^{11} + 18q^{13} + 16q^{15} + 241q^{16} + 18q^{17} - 3q^{18} + 12q^{19} - 2q^{20} + 32q^{21} - 4q^{22} - q^{23} - 4q^{24} + 243q^{25} - 2q^{26} + 8q^{28} + 6q^{29} - 24q^{30} + 16q^{31} + q^{32} - 12q^{33} + 2q^{34} + 4q^{35} + 257q^{36} + 22q^{37} - 12q^{38} + 36q^{39} + 6q^{40} - 14q^{41} + 4q^{43} + 4q^{44} + 58q^{45} + 3q^{46} + 249q^{49} + 39q^{50} + 16q^{51} + 18q^{52} + 18q^{53} - 40q^{54} - 40q^{55} + 40q^{57} + 2q^{58} - 16q^{59} + 16q^{60} + 38q^{61} + 8q^{62} + 28q^{63} + 241q^{64} + 20q^{65} + 16q^{66} - 4q^{67} + 18q^{68} - 4q^{69} - 48q^{70} + 8q^{71} - 3q^{72} + 18q^{73} - 2q^{74} - 12q^{75} + 12q^{76} - 8q^{77} + 8q^{78} + 40q^{79} - 2q^{80} + 297q^{81} + 2q^{82} + 4q^{83} + 32q^{84} + 4q^{85} - 12q^{86} + 24q^{87} - 4q^{88} - 34q^{89} - 2q^{90} + 56q^{91} - q^{92} + 56q^{93} - 16q^{94} + 32q^{95} - 4q^{96} + 10q^{97} + 25q^{98} - 12q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 23 131
6026.2.a.a \(1\) \(48.118\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{8}-3q^{9}+2q^{11}-2q^{13}+\cdots\)
6026.2.a.b \(1\) \(48.118\) \(\Q\) None \(-1\) \(0\) \(3\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+3q^{5}-2q^{7}-q^{8}-3q^{9}+\cdots\)
6026.2.a.c \(1\) \(48.118\) \(\Q\) None \(1\) \(-2\) \(3\) \(2\) \(-\) \(+\) \(-\) \(q+q^{2}-2q^{3}+q^{4}+3q^{5}-2q^{6}+2q^{7}+\cdots\)
6026.2.a.d \(1\) \(48.118\) \(\Q\) None \(1\) \(2\) \(-1\) \(2\) \(-\) \(+\) \(-\) \(q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}+2q^{7}+\cdots\)
6026.2.a.e \(2\) \(48.118\) \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(0\) \(4\) \(-\) \(+\) \(+\) \(q+q^{2}+(1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\beta )q^{6}+\cdots\)
6026.2.a.f \(20\) \(48.118\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(20\) \(-5\) \(-6\) \(-12\) \(-\) \(-\) \(+\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\)
6026.2.a.g \(21\) \(48.118\) None \(21\) \(0\) \(-13\) \(-18\) \(-\) \(+\) \(-\)
6026.2.a.h \(24\) \(48.118\) None \(-24\) \(-1\) \(-1\) \(-7\) \(+\) \(+\) \(+\)
6026.2.a.i \(25\) \(48.118\) None \(-25\) \(-4\) \(-3\) \(-11\) \(+\) \(-\) \(-\)
6026.2.a.j \(33\) \(48.118\) None \(-33\) \(3\) \(-4\) \(11\) \(+\) \(-\) \(+\)
6026.2.a.k \(35\) \(48.118\) None \(35\) \(-3\) \(10\) \(14\) \(-\) \(+\) \(+\)
6026.2.a.l \(36\) \(48.118\) None \(-36\) \(4\) \(1\) \(13\) \(+\) \(+\) \(-\)
6026.2.a.m \(41\) \(48.118\) None \(41\) \(4\) \(9\) \(12\) \(-\) \(-\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6026))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6026)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(131))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(262))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3013))\)\(^{\oplus 2}\)