Properties

Label 6046.2.a
Level 6046
Weight 2
Character orbit a
Rep. character \(\chi_{6046}(1,\cdot)\)
Character field \(\Q\)
Dimension 251
Newforms 7
Sturm bound 1512
Trace bound 11

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Defining parameters

Level: \( N \) = \( 6046 = 2 \cdot 3023 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6046.a (trivial)
Character field: \(\Q\)
Newforms: \( 7 \)
Sturm bound: \(1512\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6046))\).

Total New Old
Modular forms 758 251 507
Cusp forms 755 251 504
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.

\(2\)\(3023\)FrickeDim.
\(+\)\(+\)\(+\)\(56\)
\(+\)\(-\)\(-\)\(70\)
\(-\)\(+\)\(-\)\(69\)
\(-\)\(-\)\(+\)\(56\)
Plus space\(+\)\(112\)
Minus space\(-\)\(139\)

Trace form

\(251q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 251q^{4} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 255q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(251q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 251q^{4} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 255q^{9} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 251q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 8q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 249q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut -\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 12q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut -\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 255q^{36} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 20q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut +\mathstrut 12q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut +\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 32q^{45} \) \(\mathstrut -\mathstrut 24q^{47} \) \(\mathstrut +\mathstrut 231q^{49} \) \(\mathstrut -\mathstrut 7q^{50} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 8q^{53} \) \(\mathstrut -\mathstrut 12q^{54} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 4q^{56} \) \(\mathstrut -\mathstrut 24q^{57} \) \(\mathstrut -\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 88q^{63} \) \(\mathstrut +\mathstrut 251q^{64} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut -\mathstrut 6q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 8q^{70} \) \(\mathstrut -\mathstrut 5q^{72} \) \(\mathstrut -\mathstrut 42q^{73} \) \(\mathstrut -\mathstrut 18q^{74} \) \(\mathstrut -\mathstrut 20q^{75} \) \(\mathstrut -\mathstrut 8q^{76} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 8q^{78} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 283q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut -\mathstrut 8q^{84} \) \(\mathstrut -\mathstrut 52q^{85} \) \(\mathstrut +\mathstrut 6q^{86} \) \(\mathstrut -\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 6q^{88} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 4q^{90} \) \(\mathstrut -\mathstrut 20q^{91} \) \(\mathstrut -\mathstrut 4q^{92} \) \(\mathstrut -\mathstrut 20q^{93} \) \(\mathstrut +\mathstrut 12q^{94} \) \(\mathstrut +\mathstrut 16q^{95} \) \(\mathstrut -\mathstrut 10q^{97} \) \(\mathstrut +\mathstrut 15q^{98} \) \(\mathstrut -\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6046))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3023
6046.2.a.a \(1\) \(48.278\) \(\Q\) None \(-1\) \(2\) \(-2\) \(2\) \(+\) \(-\) \(q-q^{2}+2q^{3}+q^{4}-2q^{5}-2q^{6}+2q^{7}+\cdots\)
6046.2.a.b \(1\) \(48.278\) \(\Q\) None \(-1\) \(2\) \(-2\) \(2\) \(+\) \(+\) \(q-q^{2}+2q^{3}+q^{4}-2q^{5}-2q^{6}+2q^{7}+\cdots\)
6046.2.a.c \(2\) \(48.278\) \(\Q(\sqrt{5}) \) None \(2\) \(-3\) \(-6\) \(-5\) \(-\) \(+\) \(q+q^{2}+(-1-\beta )q^{3}+q^{4}-3q^{5}+(-1+\cdots)q^{6}+\cdots\)
6046.2.a.d \(55\) \(48.278\) None \(-55\) \(-4\) \(-7\) \(17\) \(+\) \(+\)
6046.2.a.e \(56\) \(48.278\) None \(56\) \(-18\) \(-17\) \(-35\) \(-\) \(-\)
6046.2.a.f \(67\) \(48.278\) None \(67\) \(21\) \(21\) \(38\) \(-\) \(+\)
6046.2.a.g \(69\) \(48.278\) None \(-69\) \(0\) \(13\) \(-27\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6046))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6046)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(3023))\)\(^{\oplus 2}\)