Properties

Label 33.14.a
Level $33$
Weight $14$
Character orbit 33.a
Rep. character $\chi_{33}(1,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $5$
Sturm bound $56$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 33.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(56\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(33))\).

Total New Old
Modular forms 54 20 34
Cusp forms 50 20 30
Eisenstein series 4 0 4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(11\)FrickeDim
\(+\)\(+\)$+$\(5\)
\(+\)\(-\)$-$\(6\)
\(-\)\(+\)$-$\(5\)
\(-\)\(-\)$+$\(4\)
Plus space\(+\)\(9\)
Minus space\(-\)\(11\)

Trace form

\( 20 q + 128 q^{2} - 1458 q^{3} + 82284 q^{4} - 83728 q^{5} + 154548 q^{6} + 215484 q^{7} + 3726612 q^{8} + 10628820 q^{9} + O(q^{10}) \) \( 20 q + 128 q^{2} - 1458 q^{3} + 82284 q^{4} - 83728 q^{5} + 154548 q^{6} + 215484 q^{7} + 3726612 q^{8} + 10628820 q^{9} - 11908976 q^{10} - 17915904 q^{12} - 20283240 q^{13} + 131354084 q^{14} - 45562500 q^{15} + 191568948 q^{16} + 357515588 q^{17} + 68024448 q^{18} - 196661812 q^{19} - 1624637732 q^{20} + 716452452 q^{21} - 226759808 q^{22} - 156952640 q^{23} + 2893602204 q^{24} + 5709168396 q^{25} + 1569938300 q^{26} - 774840978 q^{27} + 958880464 q^{28} + 3845627028 q^{29} + 10841699664 q^{30} + 686582952 q^{31} + 10045776172 q^{32} - 2582935938 q^{33} - 43230545888 q^{34} + 21814169672 q^{35} + 43729091244 q^{36} - 55280506744 q^{37} + 63604617504 q^{38} + 45566923572 q^{39} - 140821350312 q^{40} - 19363855060 q^{41} + 65504478708 q^{42} - 32583510124 q^{43} - 102793055464 q^{44} - 44496492048 q^{45} + 237230620400 q^{46} + 3713807272 q^{47} + 79102530288 q^{48} + 315636257460 q^{49} + 73830763696 q^{50} - 362593204272 q^{51} + 44644454824 q^{52} + 408834210504 q^{53} + 82133143668 q^{54} - 221445125000 q^{55} + 864442297860 q^{56} - 421995661380 q^{57} + 468462887160 q^{58} + 1182585580192 q^{59} + 434624909868 q^{60} + 305485068080 q^{61} - 1305561116488 q^{62} + 114517032444 q^{63} + 4395550456652 q^{64} - 4046326088032 q^{65} - 330615800064 q^{66} + 501560235928 q^{67} - 76816014248 q^{68} - 419633815104 q^{69} - 831141795896 q^{70} - 2048034853368 q^{71} + 1980474407892 q^{72} + 3914474360016 q^{73} - 7524849955464 q^{74} - 1396652793966 q^{75} - 762713395216 q^{76} + 871827685564 q^{77} - 225294245316 q^{78} + 4194265822348 q^{79} + 6547137056284 q^{80} + 5648590729620 q^{81} - 20679836834720 q^{82} - 12053563744104 q^{83} - 3502848837456 q^{84} - 10398121235960 q^{85} + 12832388017656 q^{86} + 2359260629640 q^{87} - 817036846956 q^{88} - 13447931038104 q^{89} - 6328918114416 q^{90} + 220683788936 q^{91} + 6496363461020 q^{92} + 1075820169528 q^{93} - 43818960030496 q^{94} - 19526879662008 q^{95} + 23529116464596 q^{96} + 35516139685816 q^{97} + 42400731736800 q^{98} + O(q^{100}) \)

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(33))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 11
33.14.a.a 33.a 1.a $1$ $35.386$ \(\Q\) None \(140\) \(729\) \(48740\) \(487486\) $-$ $+$ $\mathrm{SU}(2)$ \(q+140q^{2}+3^{6}q^{3}+11408q^{4}+48740q^{5}+\cdots\)
33.14.a.b 33.a 1.a $4$ $35.386$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-11\) \(2916\) \(-83432\) \(69652\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-3+\beta _{1})q^{2}+3^{6}q^{3}+(-1564+\cdots)q^{4}+\cdots\)
33.14.a.c 33.a 1.a $4$ $35.386$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(41\) \(2916\) \(-38422\) \(41998\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(10+\beta _{1})q^{2}+3^{6}q^{3}+(5909+43\beta _{1}+\cdots)q^{4}+\cdots\)
33.14.a.d 33.a 1.a $5$ $35.386$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-53\) \(-3645\) \(10318\) \(-667804\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-11+\beta _{1})q^{2}-3^{6}q^{3}+(7020-11\beta _{1}+\cdots)q^{4}+\cdots\)
33.14.a.e 33.a 1.a $6$ $35.386$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(11\) \(-4374\) \(-20932\) \(284152\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{2}-3^{6}q^{3}+(3061-10\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(33))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_0(33)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)