Properties

Label 4.7.b
Level 4
Weight 7
Character orbit b
Rep. character \(\chi_{4}(3,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 3
Trace bound 0

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Defining parameters

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

Dimensions

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

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

Trace form

\( 2q + 4q^{2} - 112q^{4} + 20q^{5} + 480q^{6} - 704q^{8} - 462q^{9} + O(q^{10}) \) \( 2q + 4q^{2} - 112q^{4} + 20q^{5} + 480q^{6} - 704q^{8} - 462q^{9} + 40q^{10} + 1920q^{12} + 2932q^{13} - 4800q^{14} + 4352q^{16} - 9532q^{17} - 924q^{18} - 1120q^{20} + 19200q^{21} + 14880q^{22} - 23040q^{24} - 31050q^{25} + 5864q^{26} - 19200q^{28} + 50996q^{29} + 4800q^{30} + 62464q^{32} - 59520q^{33} - 19064q^{34} + 25872q^{36} + 3988q^{37} - 116640q^{38} - 7040q^{40} + 58724q^{41} + 38400q^{42} + 59520q^{44} - 4620q^{45} + 162240q^{46} - 215040q^{48} + 43298q^{49} - 62100q^{50} - 164192q^{52} - 385708q^{53} + 239040q^{54} + 230400q^{56} + 466560q^{57} + 101992q^{58} + 19200q^{60} - 21836q^{61} - 648960q^{62} - 28672q^{64} + 29320q^{65} - 119040q^{66} + 533792q^{68} - 648960q^{69} - 48000q^{70} + 162624q^{72} + 577252q^{73} + 7976q^{74} - 466560q^{76} + 595200q^{77} + 703680q^{78} + 43520q^{80} - 1292958q^{81} + 117448q^{82} - 1075200q^{84} - 95320q^{85} + 333600q^{86} - 714240q^{88} + 621476q^{89} - 9240q^{90} + 648960q^{92} + 2595840q^{93} + 117120q^{94} + 614400q^{96} - 2914172q^{97} + 86596q^{98} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4.7.b.a \(2\) \(0.920\) \(\Q(\sqrt{-15}) \) None \(4\) \(0\) \(20\) \(0\) \(q+(2+\beta )q^{2}-4\beta q^{3}+(-56+4\beta )q^{4}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 4 T + 64 T^{2} \)
$3$ \( 1 - 498 T^{2} + 531441 T^{4} \)
$5$ \( ( 1 - 10 T + 15625 T^{2} )^{2} \)
$7$ \( 1 - 139298 T^{2} + 13841287201 T^{4} \)
$11$ \( 1 - 2620562 T^{2} + 3138428376721 T^{4} \)
$13$ \( ( 1 - 1466 T + 4826809 T^{2} )^{2} \)
$17$ \( ( 1 + 4766 T + 24137569 T^{2} )^{2} \)
$19$ \( 1 - 37404722 T^{2} + 2213314919066161 T^{4} \)
$23$ \( 1 - 186397538 T^{2} + 21914624432020321 T^{4} \)
$29$ \( ( 1 - 25498 T + 594823321 T^{2} )^{2} \)
$31$ \( 1 - 20219522 T^{2} + 787662783788549761 T^{4} \)
$37$ \( ( 1 - 1994 T + 2565726409 T^{2} )^{2} \)
$41$ \( ( 1 - 29362 T + 4750104241 T^{2} )^{2} \)
$43$ \( 1 - 12179022098 T^{2} + 39959630797262576401 T^{4} \)
$47$ \( 1 - 21501276098 T^{2} + \)\(11\!\cdots\!41\)\( T^{4} \)
$53$ \( ( 1 + 192854 T + 22164361129 T^{2} )^{2} \)
$59$ \( 1 - 78211344722 T^{2} + \)\(17\!\cdots\!81\)\( T^{4} \)
$61$ \( ( 1 + 10918 T + 51520374361 T^{2} )^{2} \)
$67$ \( 1 - 25565876978 T^{2} + \)\(81\!\cdots\!61\)\( T^{4} \)
$71$ \( 1 + 27079768798 T^{2} + \)\(16\!\cdots\!41\)\( T^{4} \)
$73$ \( ( 1 - 288626 T + 151334226289 T^{2} )^{2} \)
$79$ \( 1 - 389636558402 T^{2} + \)\(59\!\cdots\!41\)\( T^{4} \)
$83$ \( 1 - 612202422578 T^{2} + \)\(10\!\cdots\!61\)\( T^{4} \)
$89$ \( ( 1 - 310738 T + 496981290961 T^{2} )^{2} \)
$97$ \( ( 1 + 1457086 T + 832972004929 T^{2} )^{2} \)
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