Properties

Label 6046.2.a
Level 6046
Weight 2
Character orbit a
Rep. character \(\chi_{6046}(1,\cdot)\)
Character field \(\Q\)
Dimension 251
Newform subspaces 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: \(\Q\)
Newform subspaces: \( 7 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6046))\) into newform subspaces

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

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( ( 1 - T )^{2} \))
$3$ (\( 1 - 2 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 + 3 T + 7 T^{2} + 9 T^{3} + 9 T^{4} \))
$5$ (\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( ( 1 + 3 T + 5 T^{2} )^{2} \))
$7$ (\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 5 T + 19 T^{2} + 35 T^{3} + 49 T^{4} \))
$11$ (\( 1 + 5 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 3 T + 23 T^{2} + 33 T^{3} + 121 T^{4} \))
$13$ (\( 1 + 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 8 T + 37 T^{2} + 104 T^{3} + 169 T^{4} \))
$17$ (\( 1 - 4 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( ( 1 + 5 T + 17 T^{2} )^{2} \))
$19$ (\( 1 + 6 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 11 T + 67 T^{2} + 209 T^{3} + 361 T^{4} \))
$23$ (\( 1 - 6 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 8 T + 57 T^{2} + 184 T^{3} + 529 T^{4} \))
$29$ (\( 1 + 3 T + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))(\( 1 - 2 T + 54 T^{2} - 58 T^{3} + 841 T^{4} \))
$31$ (\( 1 - 9 T + 31 T^{2} \))(\( 1 - 3 T + 31 T^{2} \))(\( 1 + 42 T^{2} + 961 T^{4} \))
$37$ (\( 1 - 5 T + 37 T^{2} \))(\( 1 - T + 37 T^{2} \))(\( 1 + 6 T + 63 T^{2} + 222 T^{3} + 1369 T^{4} \))
$41$ (\( 1 - 6 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 + 13 T + 93 T^{2} + 533 T^{3} + 1681 T^{4} \))
$43$ (\( 1 + 7 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 - 3 T + 77 T^{2} - 129 T^{3} + 1849 T^{4} \))
$47$ (\( 1 - 4 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 6 T + 83 T^{2} + 282 T^{3} + 2209 T^{4} \))
$53$ (\( 1 - 10 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - T + 105 T^{2} - 53 T^{3} + 2809 T^{4} \))
$59$ (\( 1 + 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 8 T + 89 T^{2} + 472 T^{3} + 3481 T^{4} \))
$61$ (\( 1 - 5 T + 61 T^{2} \))(\( 1 - T + 61 T^{2} \))(\( 1 + 7 T + 103 T^{2} + 427 T^{3} + 3721 T^{4} \))
$67$ (\( 1 + 2 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( ( 1 + 8 T + 67 T^{2} )^{2} \))
$71$ (\( 1 - 10 T + 71 T^{2} \))(\( 1 - 2 T + 71 T^{2} \))(\( 1 - 6 T + 106 T^{2} - 426 T^{3} + 5041 T^{4} \))
$73$ (\( 1 + 4 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 + 66 T^{2} + 5329 T^{4} \))
$79$ (\( 1 + 11 T + 79 T^{2} \))(\( 1 + T + 79 T^{2} \))(\( 1 - 10 T + 163 T^{2} - 790 T^{3} + 6241 T^{4} \))
$83$ (\( 1 - 2 T + 83 T^{2} \))(\( 1 + 14 T + 83 T^{2} \))(\( 1 + 8 T + 102 T^{2} + 664 T^{3} + 6889 T^{4} \))
$89$ (\( 1 - 18 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 158 T^{2} + 7921 T^{4} \))
$97$ (\( 1 - 3 T + 97 T^{2} \))(\( 1 - 3 T + 97 T^{2} \))(\( 1 + 4 T + 178 T^{2} + 388 T^{3} + 9409 T^{4} \))
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