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Properties

Label 44.5.b
Level $44$
Weight $5$
Character orbit 44.b
Rep. character $\chi_{44}(23,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $1$
Sturm bound $30$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 44 = 2^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 44.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(30\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(44, [\chi])\).

Total New Old
Modular forms 26 20 6
Cusp forms 22 20 2
Eisenstein series 4 0 4

Trace form

\( 20 q - 28 q^{4} + 24 q^{5} + 30 q^{6} + 36 q^{8} - 540 q^{9} + O(q^{10}) \) \( 20 q - 28 q^{4} + 24 q^{5} + 30 q^{6} + 36 q^{8} - 540 q^{9} - 298 q^{10} - 200 q^{12} + 472 q^{13} - 372 q^{14} - 200 q^{16} - 600 q^{17} + 1586 q^{18} + 624 q^{20} + 320 q^{21} - 492 q^{24} + 3340 q^{25} - 1140 q^{26} + 1880 q^{28} - 1896 q^{29} - 2346 q^{30} + 2880 q^{32} + 6376 q^{34} - 5620 q^{36} - 680 q^{37} - 1560 q^{38} - 2508 q^{40} + 1800 q^{41} - 2380 q^{42} - 1452 q^{44} - 1976 q^{45} - 1130 q^{46} + 504 q^{48} - 11372 q^{49} - 7278 q^{50} + 10976 q^{52} - 2520 q^{53} + 1402 q^{54} - 10200 q^{56} + 7712 q^{57} + 5956 q^{58} + 12296 q^{60} + 18040 q^{61} + 8046 q^{62} + 560 q^{64} - 6768 q^{65} - 1210 q^{66} - 20064 q^{68} - 8528 q^{69} + 972 q^{70} + 4440 q^{72} + 6120 q^{73} - 1470 q^{74} - 8280 q^{76} + 7064 q^{78} + 25704 q^{80} - 7980 q^{81} - 20500 q^{82} - 2968 q^{84} + 20496 q^{85} - 23940 q^{86} + 7260 q^{88} + 12408 q^{89} + 8360 q^{90} - 21144 q^{92} - 720 q^{93} + 27824 q^{94} + 13552 q^{96} + 26520 q^{97} + 43560 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(44, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
44.5.b.a 44.b 4.b $20$ $4.548$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None 44.5.b.a \(0\) \(0\) \(24\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(44, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(44, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)