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Properties

Label 21.33.b
Level $21$
Weight $33$
Character orbit 21.b
Rep. character $\chi_{21}(8,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $1$
Sturm bound $88$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 33 \)
Character orbit: \([\chi]\) \(=\) 21.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(88\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{33}(21, [\chi])\).

Total New Old
Modular forms 88 64 24
Cusp forms 84 64 20
Eisenstein series 4 0 4

Trace form

\( 64 q + 42774298 q^{3} - 128804556708 q^{4} + 933804622814 q^{6} - 2661709321929080 q^{9} + O(q^{10}) \) \( 64 q + 42774298 q^{3} - 128804556708 q^{4} + 933804622814 q^{6} - 2661709321929080 q^{9} + 12700458777826876 q^{10} + 16560668213315618 q^{12} - 779662097386845540 q^{13} + 27876123863063359876 q^{15} + 228871642891389581316 q^{16} + 521413503785997440888 q^{18} - 681706881337157521692 q^{19} - 431503881158008113826 q^{21} + 19120468187392744108144 q^{22} - 45125095777673694858054 q^{24} - 237119983579497521268264 q^{25} + 74365326375203190687598 q^{27} - 260996322622686644022008 q^{28} + 852759618763392319765868 q^{30} - 1358180324906510744611784 q^{31} + 167404755195681713530156 q^{33} + 10642186773288746488261680 q^{34} - 11711812793758939011321604 q^{36} + 63659724279901954174127200 q^{37} + 20360640903448602426342556 q^{39} - 266207532467737680346702140 q^{40} + 96091334734695477693967150 q^{42} - 24813883332284263694074960 q^{43} - 295070024428567568989268180 q^{45} - 918028865892271951694570448 q^{46} - 6300988561174358262351979762 q^{48} + 10097624450230131623362735552 q^{49} - 4622010869824749895266142284 q^{51} + 17159412300004978195879866788 q^{52} - 6673593378082253401307883466 q^{54} + 2442354815144746218376572584 q^{55} + 2378509030520646137537303296 q^{57} + 190077506986526245795566340336 q^{58} - 374115780186052983158362561348 q^{60} + 99766669274989725702936459924 q^{61} - 30712401990673050365871429556 q^{63} + 400943516045473601608812787636 q^{64} - 720581678602395470219517737068 q^{66} + 73852404789389472034372092840 q^{67} - 1918774447093691762779494646608 q^{69} + 411148821544167628017331107740 q^{70} - 5739782432693959795949031524256 q^{72} + 3915537814122658222047778895512 q^{73} - 5610513809660665161777257057146 q^{75} + 15527044450561930247763678447284 q^{76} - 8815089651936141495775983174628 q^{78} - 1756119931827678230469250976128 q^{79} - 1723294285320428987738283283928 q^{81} - 26570441417976029198788879753576 q^{82} + 3988641463277435045591806322194 q^{84} - 13918207634511949564944022475904 q^{85} + 4214670677854102763671028064004 q^{87} - 41766265169004456915366483222312 q^{88} + 45890754779166227082585780071648 q^{90} - 28370228500765093177423738459588 q^{91} + 102872460014017329227733357232008 q^{93} - 344540199084263505892210158281184 q^{94} + 705553200246779133797316737679382 q^{96} - 501176499990824103029916368159648 q^{97} + 432901556854707300232201533648688 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{33}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
21.33.b.a 21.b 3.b $64$ $136.220$ None \(0\) \(42774298\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{33}^{\mathrm{old}}(21, [\chi])\) into lower level spaces

\( S_{33}^{\mathrm{old}}(21, [\chi]) \cong \) \(S_{33}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)