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Properties

Label 7.4.c
Level 7
Weight 4
Character orbit c
Rep. character \(\chi_{7}(2,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 2
Newform subspaces 1
Sturm bound 2
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 7.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(7, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

Trace form

\( 2q - 2q^{2} - 7q^{3} + 4q^{4} - 7q^{5} + 28q^{6} + 28q^{7} - 48q^{8} - 22q^{9} + O(q^{10}) \) \( 2q - 2q^{2} - 7q^{3} + 4q^{4} - 7q^{5} + 28q^{6} + 28q^{7} - 48q^{8} - 22q^{9} - 14q^{10} + 5q^{11} + 28q^{12} - 28q^{13} + 14q^{14} + 98q^{15} + 16q^{16} + 21q^{17} - 44q^{18} - 49q^{19} - 56q^{20} - 245q^{21} - 20q^{22} + 159q^{23} + 168q^{24} + 76q^{25} + 28q^{26} - 70q^{27} + 140q^{28} + 116q^{29} - 98q^{30} - 147q^{31} - 160q^{32} + 35q^{33} - 84q^{34} + 49q^{35} - 176q^{36} - 219q^{37} - 98q^{38} + 98q^{39} + 168q^{40} + 700q^{41} + 392q^{42} - 248q^{43} - 20q^{44} - 154q^{45} + 318q^{46} - 525q^{47} - 224q^{48} + 98q^{49} - 304q^{50} + 147q^{51} - 56q^{52} - 303q^{53} + 70q^{54} - 70q^{55} - 672q^{56} + 686q^{57} - 116q^{58} + 105q^{59} + 196q^{60} + 413q^{61} + 588q^{62} + 154q^{63} + 896q^{64} + 98q^{65} + 70q^{66} - 415q^{67} - 84q^{68} - 2226q^{69} - 490q^{70} - 864q^{71} + 528q^{72} + 1113q^{73} - 438q^{74} + 532q^{75} - 392q^{76} + 175q^{77} - 392q^{78} + 103q^{79} + 112q^{80} + 839q^{81} - 700q^{82} + 2184q^{83} - 196q^{84} - 294q^{85} + 248q^{86} - 406q^{87} - 120q^{88} + 329q^{89} + 616q^{90} - 392q^{91} + 1272q^{92} - 1029q^{93} - 1050q^{94} - 343q^{95} - 1120q^{96} - 1764q^{97} + 1078q^{98} - 220q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(7, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7.4.c.a \(2\) \(0.413\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-7\) \(-7\) \(28\) \(q+(-2+2\zeta_{6})q^{2}-7\zeta_{6}q^{3}+4\zeta_{6}q^{4}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T - 4 T^{2} + 16 T^{3} + 64 T^{4} \)
$3$ \( 1 + 7 T + 22 T^{2} + 189 T^{3} + 729 T^{4} \)
$5$ \( 1 + 7 T - 76 T^{2} + 875 T^{3} + 15625 T^{4} \)
$7$ \( 1 - 28 T + 343 T^{2} \)
$11$ \( 1 - 5 T - 1306 T^{2} - 6655 T^{3} + 1771561 T^{4} \)
$13$ \( ( 1 + 14 T + 2197 T^{2} )^{2} \)
$17$ \( 1 - 21 T - 4472 T^{2} - 103173 T^{3} + 24137569 T^{4} \)
$19$ \( 1 + 49 T - 4458 T^{2} + 336091 T^{3} + 47045881 T^{4} \)
$23$ \( 1 - 159 T + 13114 T^{2} - 1934553 T^{3} + 148035889 T^{4} \)
$29$ \( ( 1 - 58 T + 24389 T^{2} )^{2} \)
$31$ \( 1 + 147 T - 8182 T^{2} + 4379277 T^{3} + 887503681 T^{4} \)
$37$ \( 1 + 219 T - 2692 T^{2} + 11093007 T^{3} + 2565726409 T^{4} \)
$41$ \( ( 1 - 350 T + 68921 T^{2} )^{2} \)
$43$ \( ( 1 + 124 T + 79507 T^{2} )^{2} \)
$47$ \( 1 + 525 T + 171802 T^{2} + 54507075 T^{3} + 10779215329 T^{4} \)
$53$ \( 1 + 303 T - 57068 T^{2} + 45109731 T^{3} + 22164361129 T^{4} \)
$59$ \( 1 - 105 T - 194354 T^{2} - 21564795 T^{3} + 42180533641 T^{4} \)
$61$ \( 1 - 413 T - 56412 T^{2} - 93743153 T^{3} + 51520374361 T^{4} \)
$67$ \( 1 + 415 T - 128538 T^{2} + 124816645 T^{3} + 90458382169 T^{4} \)
$71$ \( ( 1 + 432 T + 357911 T^{2} )^{2} \)
$73$ \( 1 - 1113 T + 849752 T^{2} - 432975921 T^{3} + 151334226289 T^{4} \)
$79$ \( 1 - 103 T - 482430 T^{2} - 50783017 T^{3} + 243087455521 T^{4} \)
$83$ \( ( 1 - 1092 T + 571787 T^{2} )^{2} \)
$89$ \( 1 - 329 T - 596728 T^{2} - 231934801 T^{3} + 496981290961 T^{4} \)
$97$ \( ( 1 + 882 T + 912673 T^{2} )^{2} \)
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