Properties

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

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 7.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(7))\).

Total New Old
Modular forms 3 1 2
Cusp forms 1 1 0
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(7\)Dim.
\(+\)\(1\)

Trace form

\( q - q^{2} - 2q^{3} - 7q^{4} + 16q^{5} + 2q^{6} - 7q^{7} + 15q^{8} - 23q^{9} + O(q^{10}) \) \( q - q^{2} - 2q^{3} - 7q^{4} + 16q^{5} + 2q^{6} - 7q^{7} + 15q^{8} - 23q^{9} - 16q^{10} - 8q^{11} + 14q^{12} + 28q^{13} + 7q^{14} - 32q^{15} + 41q^{16} + 54q^{17} + 23q^{18} - 110q^{19} - 112q^{20} + 14q^{21} + 8q^{22} + 48q^{23} - 30q^{24} + 131q^{25} - 28q^{26} + 100q^{27} + 49q^{28} - 110q^{29} + 32q^{30} + 12q^{31} - 161q^{32} + 16q^{33} - 54q^{34} - 112q^{35} + 161q^{36} - 246q^{37} + 110q^{38} - 56q^{39} + 240q^{40} + 182q^{41} - 14q^{42} + 128q^{43} + 56q^{44} - 368q^{45} - 48q^{46} + 324q^{47} - 82q^{48} + 49q^{49} - 131q^{50} - 108q^{51} - 196q^{52} - 162q^{53} - 100q^{54} - 128q^{55} - 105q^{56} + 220q^{57} + 110q^{58} + 810q^{59} + 224q^{60} - 488q^{61} - 12q^{62} + 161q^{63} - 167q^{64} + 448q^{65} - 16q^{66} + 244q^{67} - 378q^{68} - 96q^{69} + 112q^{70} - 768q^{71} - 345q^{72} - 702q^{73} + 246q^{74} - 262q^{75} + 770q^{76} + 56q^{77} + 56q^{78} + 440q^{79} + 656q^{80} + 421q^{81} - 182q^{82} - 1302q^{83} - 98q^{84} + 864q^{85} - 128q^{86} + 220q^{87} - 120q^{88} + 730q^{89} + 368q^{90} - 196q^{91} - 336q^{92} - 24q^{93} - 324q^{94} - 1760q^{95} + 322q^{96} + 294q^{97} - 49q^{98} + 184q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7
7.4.a.a \(1\) \(0.413\) \(\Q\) None \(-1\) \(-2\) \(16\) \(-7\) \(+\) \(q-q^{2}-2q^{3}-7q^{4}+2^{4}q^{5}+2q^{6}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T + 8 T^{2} \)
$3$ \( 1 + 2 T + 27 T^{2} \)
$5$ \( 1 - 16 T + 125 T^{2} \)
$7$ \( 1 + 7 T \)
$11$ \( 1 + 8 T + 1331 T^{2} \)
$13$ \( 1 - 28 T + 2197 T^{2} \)
$17$ \( 1 - 54 T + 4913 T^{2} \)
$19$ \( 1 + 110 T + 6859 T^{2} \)
$23$ \( 1 - 48 T + 12167 T^{2} \)
$29$ \( 1 + 110 T + 24389 T^{2} \)
$31$ \( 1 - 12 T + 29791 T^{2} \)
$37$ \( 1 + 246 T + 50653 T^{2} \)
$41$ \( 1 - 182 T + 68921 T^{2} \)
$43$ \( 1 - 128 T + 79507 T^{2} \)
$47$ \( 1 - 324 T + 103823 T^{2} \)
$53$ \( 1 + 162 T + 148877 T^{2} \)
$59$ \( 1 - 810 T + 205379 T^{2} \)
$61$ \( 1 + 488 T + 226981 T^{2} \)
$67$ \( 1 - 244 T + 300763 T^{2} \)
$71$ \( 1 + 768 T + 357911 T^{2} \)
$73$ \( 1 + 702 T + 389017 T^{2} \)
$79$ \( 1 - 440 T + 493039 T^{2} \)
$83$ \( 1 + 1302 T + 571787 T^{2} \)
$89$ \( 1 - 730 T + 704969 T^{2} \)
$97$ \( 1 - 294 T + 912673 T^{2} \)
show more
show less