Properties

Label 6015.2.a
Level 6015
Weight 2
Character orbit a
Rep. character \(\chi_{6015}(1,\cdot)\)
Character field \(\Q\)
Dimension 267
Newforms 9
Sturm bound 1608
Trace bound 2

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Defining parameters

Level: \( N \) = \( 6015 = 3 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6015.a (trivial)
Character field: \(\Q\)
Newforms: \( 9 \)
Sturm bound: \(1608\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6015))\).

Total New Old
Modular forms 808 267 541
Cusp forms 801 267 534
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.

\(3\)\(5\)\(401\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(36\)
\(+\)\(+\)\(-\)\(-\)\(31\)
\(+\)\(-\)\(+\)\(-\)\(36\)
\(+\)\(-\)\(-\)\(+\)\(29\)
\(-\)\(+\)\(+\)\(-\)\(39\)
\(-\)\(+\)\(-\)\(+\)\(28\)
\(-\)\(-\)\(+\)\(+\)\(23\)
\(-\)\(-\)\(-\)\(-\)\(45\)
Plus space\(+\)\(116\)
Minus space\(-\)\(151\)

Trace form

\(267q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 269q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 267q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(267q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 269q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 267q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut +\mathstrut 5q^{12} \) \(\mathstrut +\mathstrut 10q^{13} \) \(\mathstrut -\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 261q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 7q^{20} \) \(\mathstrut +\mathstrut 8q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 21q^{24} \) \(\mathstrut +\mathstrut 267q^{25} \) \(\mathstrut -\mathstrut 42q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut 23q^{32} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 42q^{34} \) \(\mathstrut +\mathstrut 269q^{36} \) \(\mathstrut +\mathstrut 26q^{37} \) \(\mathstrut +\mathstrut 12q^{38} \) \(\mathstrut +\mathstrut 10q^{39} \) \(\mathstrut -\mathstrut 3q^{40} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 24q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 44q^{44} \) \(\mathstrut -\mathstrut q^{45} \) \(\mathstrut -\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 16q^{47} \) \(\mathstrut -\mathstrut 3q^{48} \) \(\mathstrut +\mathstrut 307q^{49} \) \(\mathstrut -\mathstrut 3q^{50} \) \(\mathstrut +\mathstrut 14q^{51} \) \(\mathstrut +\mathstrut 30q^{52} \) \(\mathstrut +\mathstrut 34q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut -\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 72q^{56} \) \(\mathstrut +\mathstrut 20q^{57} \) \(\mathstrut -\mathstrut 58q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut +\mathstrut 5q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 221q^{64} \) \(\mathstrut -\mathstrut 14q^{65} \) \(\mathstrut -\mathstrut 28q^{66} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut -\mathstrut 46q^{68} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 42q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 28q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 2q^{78} \) \(\mathstrut -\mathstrut 40q^{79} \) \(\mathstrut +\mathstrut q^{80} \) \(\mathstrut +\mathstrut 267q^{81} \) \(\mathstrut -\mathstrut 62q^{82} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut +\mathstrut 32q^{84} \) \(\mathstrut +\mathstrut 14q^{85} \) \(\mathstrut -\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 10q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut +\mathstrut q^{90} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut -\mathstrut 64q^{92} \) \(\mathstrut +\mathstrut 8q^{93} \) \(\mathstrut +\mathstrut 80q^{94} \) \(\mathstrut -\mathstrut 4q^{95} \) \(\mathstrut +\mathstrut 13q^{96} \) \(\mathstrut -\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 67q^{98} \) \(\mathstrut -\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6015))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 401
6015.2.a.a \(2\) \(48.030\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(2\) \(4\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+(2-2\beta )q^{7}+\cdots\)
6015.2.a.b \(23\) \(48.030\) None \(-5\) \(23\) \(23\) \(-16\) \(-\) \(-\) \(+\)
6015.2.a.c \(28\) \(48.030\) None \(-1\) \(28\) \(-28\) \(-20\) \(-\) \(+\) \(-\)
6015.2.a.d \(29\) \(48.030\) None \(-1\) \(-29\) \(29\) \(2\) \(+\) \(-\) \(-\)
6015.2.a.e \(31\) \(48.030\) None \(6\) \(-31\) \(-31\) \(-4\) \(+\) \(+\) \(-\)
6015.2.a.f \(36\) \(48.030\) None \(-7\) \(-36\) \(-36\) \(2\) \(+\) \(+\) \(+\)
6015.2.a.g \(36\) \(48.030\) None \(0\) \(-36\) \(36\) \(-4\) \(+\) \(-\) \(+\)
6015.2.a.h \(39\) \(48.030\) None \(0\) \(39\) \(-39\) \(22\) \(-\) \(+\) \(+\)
6015.2.a.i \(43\) \(48.030\) None \(3\) \(43\) \(43\) \(14\) \(-\) \(-\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6015))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6015)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(401))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1203))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2005))\)\(^{\oplus 2}\)