Properties

Label 4.21.b
Level 4
Weight 21
Character orbit b
Rep. character \(\chi_{4}(3,\cdot)\)
Character field \(\Q\)
Dimension 9
Newforms 2
Sturm bound 10
Trace bound 1

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 21 \)
Character orbit: \([\chi]\) = 4.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 4 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(10\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(4, [\chi])\).

Total New Old
Modular forms 11 11 0
Cusp forms 9 9 0
Eisenstein series 2 2 0

Trace form

\(9q \) \(\mathstrut -\mathstrut 628q^{2} \) \(\mathstrut -\mathstrut 267504q^{4} \) \(\mathstrut -\mathstrut 738494q^{5} \) \(\mathstrut +\mathstrut 99460608q^{6} \) \(\mathstrut +\mathstrut 1103532992q^{8} \) \(\mathstrut -\mathstrut 6924577767q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut -\mathstrut 628q^{2} \) \(\mathstrut -\mathstrut 267504q^{4} \) \(\mathstrut -\mathstrut 738494q^{5} \) \(\mathstrut +\mathstrut 99460608q^{6} \) \(\mathstrut +\mathstrut 1103532992q^{8} \) \(\mathstrut -\mathstrut 6924577767q^{9} \) \(\mathstrut +\mathstrut 1611884376q^{10} \) \(\mathstrut -\mathstrut 41779799040q^{12} \) \(\mathstrut +\mathstrut 147660923874q^{13} \) \(\mathstrut -\mathstrut 200556776448q^{14} \) \(\mathstrut +\mathstrut 70138216704q^{16} \) \(\mathstrut -\mathstrut 1684556709806q^{17} \) \(\mathstrut +\mathstrut 1635822350412q^{18} \) \(\mathstrut +\mathstrut 241483768096q^{20} \) \(\mathstrut +\mathstrut 33281721747456q^{21} \) \(\mathstrut -\mathstrut 31324969489920q^{22} \) \(\mathstrut -\mathstrut 47563142934528q^{24} \) \(\mathstrut -\mathstrut 567413012949q^{25} \) \(\mathstrut -\mathstrut 63229698776360q^{26} \) \(\mathstrut +\mathstrut 385881741772800q^{28} \) \(\mathstrut +\mathstrut 303916348382242q^{29} \) \(\mathstrut -\mathstrut 1063857826698240q^{30} \) \(\mathstrut +\mathstrut 454535173225472q^{32} \) \(\mathstrut +\mathstrut 1131041167426560q^{33} \) \(\mathstrut -\mathstrut 4199565255965160q^{34} \) \(\mathstrut +\mathstrut 16320708718416912q^{36} \) \(\mathstrut -\mathstrut 7415248775263806q^{37} \) \(\mathstrut -\mathstrut 19214136907706880q^{38} \) \(\mathstrut +\mathstrut 42169382228654976q^{40} \) \(\mathstrut -\mathstrut 5755597456531022q^{41} \) \(\mathstrut -\mathstrut 92697489416232960q^{42} \) \(\mathstrut +\mathstrut 157933848933319680q^{44} \) \(\mathstrut +\mathstrut 22280783580364386q^{45} \) \(\mathstrut -\mathstrut 271527229329687552q^{46} \) \(\mathstrut +\mathstrut 485296685862666240q^{48} \) \(\mathstrut -\mathstrut 37006326729654807q^{49} \) \(\mathstrut -\mathstrut 623084159258016924q^{50} \) \(\mathstrut +\mathstrut 813052968459434784q^{52} \) \(\mathstrut +\mathstrut 132739492344115714q^{53} \) \(\mathstrut -\mathstrut 1607547577815069696q^{54} \) \(\mathstrut +\mathstrut 1749313578676543488q^{56} \) \(\mathstrut +\mathstrut 440441203792112640q^{57} \) \(\mathstrut -\mathstrut 1972695284657517096q^{58} \) \(\mathstrut +\mathstrut 2279505537583872000q^{60} \) \(\mathstrut -\mathstrut 1172450092804974942q^{61} \) \(\mathstrut -\mathstrut 1243411198213386240q^{62} \) \(\mathstrut +\mathstrut 1333510659266973696q^{64} \) \(\mathstrut -\mathstrut 828610552028041948q^{65} \) \(\mathstrut -\mathstrut 21993146403409920q^{66} \) \(\mathstrut -\mathstrut 1641594099654542816q^{68} \) \(\mathstrut +\mathstrut 3450619355851659264q^{69} \) \(\mathstrut +\mathstrut 8506721176491632640q^{70} \) \(\mathstrut -\mathstrut 19477455141526114368q^{72} \) \(\mathstrut -\mathstrut 4955973119248806606q^{73} \) \(\mathstrut +\mathstrut 23508341140743382360q^{74} \) \(\mathstrut -\mathstrut 26576303558589158400q^{76} \) \(\mathstrut -\mathstrut 5280312525070141440q^{77} \) \(\mathstrut +\mathstrut 39300720744848010240q^{78} \) \(\mathstrut -\mathstrut 53478714049403538944q^{80} \) \(\mathstrut +\mathstrut 27869130702616624425q^{81} \) \(\mathstrut +\mathstrut 59306974273770046104q^{82} \) \(\mathstrut -\mathstrut 85636060864270565376q^{84} \) \(\mathstrut +\mathstrut 5624508021574984452q^{85} \) \(\mathstrut +\mathstrut 60721004056878217728q^{86} \) \(\mathstrut -\mathstrut 36088003765030440960q^{88} \) \(\mathstrut -\mathstrut 30717207683107545998q^{89} \) \(\mathstrut +\mathstrut 14470051757664399576q^{90} \) \(\mathstrut +\mathstrut 64932970344704317440q^{92} \) \(\mathstrut -\mathstrut 53255995615294218240q^{93} \) \(\mathstrut -\mathstrut 49076400009934399488q^{94} \) \(\mathstrut +\mathstrut 148896006651003076608q^{96} \) \(\mathstrut +\mathstrut 21227709255069480594q^{97} \) \(\mathstrut -\mathstrut 274458557005261496308q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{21}^{\mathrm{new}}(4, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4.21.b.a \(1\) \(10.141\) \(\Q\) \(\Q(\sqrt{-1}) \) \(-1024\) \(0\) \(-19306574\) \(0\) \(q-2^{10}q^{2}+2^{20}q^{4}-19306574q^{5}+\cdots\)
4.21.b.b \(8\) \(10.141\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(396\) \(0\) \(18568080\) \(0\) \(q+(7^{2}+\beta _{1})q^{2}+(6-12\beta _{1}-\beta _{2})q^{3}+\cdots\)