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Properties

Label 20.19.d
Level $20$
Weight $19$
Character orbit 20.d
Rep. character $\chi_{20}(19,\cdot)$
Character field $\Q$
Dimension $52$
Newform subspaces $4$
Sturm bound $57$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 19 \)
Character orbit: \([\chi]\) \(=\) 20.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(57\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(20, [\chi])\).

Total New Old
Modular forms 56 56 0
Cusp forms 52 52 0
Eisenstein series 4 4 0

Trace form

\( 52 q - 267104 q^{4} - 860884 q^{5} + 6207296 q^{6} + 6198727820 q^{9} + O(q^{10}) \) \( 52 q - 267104 q^{4} - 860884 q^{5} + 6207296 q^{6} + 6198727820 q^{9} + 902393136 q^{10} + 10467218464 q^{14} - 3913876928 q^{16} - 230448518944 q^{20} - 520096806368 q^{21} + 8394005023424 q^{24} - 5415162839084 q^{25} - 496553046432 q^{26} - 4365686937848 q^{29} - 24582812860960 q^{30} + 98111677059648 q^{34} + 68828112611168 q^{36} - 21851693342784 q^{40} - 399424027151816 q^{41} + 1617148267411200 q^{44} - 1156790464679404 q^{45} - 569736697381024 q^{46} + 5668080956620140 q^{49} - 1355864224251744 q^{50} - 1264777868007232 q^{54} - 4711028714888384 q^{56} - 7244590810732800 q^{60} + 19024261187436824 q^{61} + 5615618264774656 q^{64} + 40641587758802112 q^{65} + 30470078435376000 q^{66} - 100169823645142112 q^{69} + 80113528508034560 q^{70} - 198008215021350432 q^{74} - 100403864699616000 q^{76} - 337070875973506624 q^{80} - 669442402593196 q^{81} + 960810295161707008 q^{84} - 41434569183984768 q^{85} + 120533042834473216 q^{86} + 881568632098403752 q^{89} + 969685889170393296 q^{90} - 4208701984503769696 q^{94} - 2522560450818521344 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{19}^{\mathrm{new}}(20, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
20.19.d.a 20.d 20.d $1$ $41.077$ \(\Q\) \(\Q(\sqrt{-5}) \) 20.19.d.a \(-512\) \(11044\) \(-1953125\) \(-41066404\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{9}q^{2}+11044q^{3}+2^{18}q^{4}-5^{9}q^{5}+\cdots\)
20.19.d.b 20.d 20.d $1$ $41.077$ \(\Q\) \(\Q(\sqrt{-5}) \) 20.19.d.a \(512\) \(-11044\) \(-1953125\) \(41066404\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{9}q^{2}-11044q^{3}+2^{18}q^{4}-5^{9}q^{5}+\cdots\)
20.19.d.c 20.d 20.d $2$ $41.077$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 20.19.d.c \(0\) \(0\) \(-1844154\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{7}iq^{2}-2^{18}q^{4}+(-922077+430441i)q^{5}+\cdots\)
20.19.d.d 20.d 20.d $48$ $41.077$ None 20.19.d.d \(0\) \(0\) \(4889520\) \(0\) $\mathrm{SU}(2)[C_{2}]$