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Properties

Label 22.4.c
Level $22$
Weight $4$
Character orbit 22.c
Rep. character $\chi_{22}(3,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $12$
Newform subspaces $2$
Sturm bound $12$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 22.c (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(22, [\chi])\).

Total New Old
Modular forms 44 12 32
Cusp forms 28 12 16
Eisenstein series 16 0 16

Trace form

\( 12 q + 2 q^{2} + 2 q^{3} - 12 q^{4} + 8 q^{5} + 42 q^{6} + 24 q^{7} + 8 q^{8} - 145 q^{9} + O(q^{10}) \) \( 12 q + 2 q^{2} + 2 q^{3} - 12 q^{4} + 8 q^{5} + 42 q^{6} + 24 q^{7} + 8 q^{8} - 145 q^{9} - 104 q^{10} - 111 q^{11} - 72 q^{12} + 98 q^{13} + 52 q^{14} + 224 q^{15} - 48 q^{16} + 184 q^{17} + 304 q^{18} - 213 q^{19} + 32 q^{20} - 280 q^{21} - 22 q^{22} + 404 q^{23} + 168 q^{24} + 109 q^{25} - 12 q^{26} + 245 q^{27} - 104 q^{28} - 392 q^{29} - 396 q^{30} + 96 q^{31} - 128 q^{32} - 1155 q^{33} - 516 q^{34} - 662 q^{35} - 40 q^{36} - 12 q^{37} - 548 q^{38} - 448 q^{39} + 224 q^{40} + 708 q^{41} + 1940 q^{42} + 2602 q^{43} + 1016 q^{44} + 2404 q^{45} - 424 q^{46} - 818 q^{47} + 32 q^{48} - 661 q^{49} + 166 q^{50} - 1579 q^{51} - 408 q^{52} - 526 q^{53} - 2288 q^{54} + 26 q^{55} + 128 q^{56} - 769 q^{57} - 916 q^{58} - 955 q^{59} - 1224 q^{60} + 718 q^{61} + 2020 q^{62} + 1064 q^{63} - 192 q^{64} + 44 q^{65} + 2656 q^{66} + 490 q^{67} + 736 q^{68} - 554 q^{69} + 24 q^{70} - 1550 q^{71} - 824 q^{72} - 1640 q^{73} - 220 q^{74} - 3561 q^{75} - 712 q^{76} + 498 q^{77} - 2320 q^{78} + 748 q^{79} - 512 q^{80} + 3006 q^{81} + 62 q^{82} + 2829 q^{83} + 2400 q^{84} - 148 q^{85} + 2186 q^{86} + 3792 q^{87} + 472 q^{88} - 474 q^{89} + 1640 q^{90} + 4278 q^{91} - 1624 q^{92} + 7052 q^{93} - 1040 q^{94} - 720 q^{95} - 128 q^{96} - 3109 q^{97} - 4776 q^{98} - 7867 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(22, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
22.4.c.a 22.c 11.c $4$ $1.298$ \(\Q(\zeta_{10})\) None \(-2\) \(-1\) \(3\) \(25\) $\mathrm{SU}(2)[C_{5}]$ \(q-2\zeta_{10}q^{2}+(-3+3\zeta_{10}+8\zeta_{10}^{3})q^{3}+\cdots\)
22.4.c.b 22.c 11.c $8$ $1.298$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(4\) \(3\) \(5\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q-2\beta _{3}q^{2}+(1+\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(22, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(22, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)