Properties

Label 9.34.a
Level $9$
Weight $34$
Character orbit 9.a
Rep. character $\chi_{9}(1,\cdot)$
Character field $\Q$
Dimension $13$
Newform subspaces $5$
Sturm bound $34$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 9 = 3^{2} \)
Weight: \( k \) \(=\) \( 34 \)
Character orbit: \([\chi]\) \(=\) 9.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(34\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_0(9))\).

Total New Old
Modular forms 35 14 21
Cusp forms 31 13 18
Eisenstein series 4 1 3

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

\(3\)Dim.
\(+\)\(5\)
\(-\)\(8\)

Trace form

\( 13q - 56142q^{2} + 53633173972q^{4} + 390287748744q^{5} - 107655133710412q^{7} - 141750813200328q^{8} + O(q^{10}) \) \( 13q - 56142q^{2} + 53633173972q^{4} + 390287748744q^{5} - 107655133710412q^{7} - 141750813200328q^{8} + 41721262498430964q^{10} + 315134302644327672q^{11} - 4077405261304652278q^{13} + 16120066026467234160q^{14} - 19889115746443509488q^{16} + 338014546645767037920q^{17} - 2872545341365213640128q^{19} + 7143086276713823673096q^{20} - 25601985333360456360120q^{22} - 43519813073967960660384q^{23} + 608812003684751267368831q^{25} - 513670979755066512693636q^{26} - 2287622089837723403924704q^{28} + 1762040027254299040430136q^{29} - 2164406515485536383559740q^{31} + 7085963980857000195497952q^{32} - 16375507709150094397869636q^{34} - 29160427299772125424359600q^{35} + 72686915097501411669613598q^{37} - 101971052475864423726166776q^{38} - 329513958539426776384606032q^{40} - 195071427858537125251683840q^{41} + 239425334111914099817637968q^{43} + 3196119697099814485785418128q^{44} - 6323936073932155024575382320q^{46} + 1415864635019240218321890384q^{47} + 24470841345336684116625381429q^{49} + 173474809095426401467167246q^{50} - 33288334913012760271408096360q^{52} + 30719588726407848868199802456q^{53} - 72823027057316817848956415664q^{55} + 415664536380890792768679291840q^{56} - 227215348897735086114902979708q^{58} + 423769002557660888461557488712q^{59} - 424929570580379694930956942986q^{61} + 925133225589425568985735790304q^{62} - 1679652092984350132966828720064q^{64} + 4463402424830186915898666494352q^{65} - 2151851002260498419256577615240q^{67} + 15145380242402908186957866218136q^{68} - 16391456048891921635691693327520q^{70} + 22482835532335836549577922554944q^{71} - 6341617609808235618332179719586q^{73} + 51222300354721542971058199627500q^{74} - 24986175866470799827323525444592q^{76} + 48349671399135940876511497658784q^{77} - 30278927593930380745328568091900q^{79} + 184648181534565699979716517335456q^{80} - 95859220347927750427779957373044q^{82} + 117154144343911374157197231342504q^{83} - 138492827138121303786042725151408q^{85} + 193145914668998844025900678574712q^{86} - 125127315653340800934056055130272q^{88} - 113439626711013745481857544269872q^{89} + 481392637302899971942623113285320q^{91} - 1067120356115364860298368188083168q^{92} + 1028117072666439501928213918437216q^{94} - 1753083991909830800400102866607984q^{95} + 788688271728588981141795118484150q^{97} - 4158200108150049253323310246794078q^{98} + O(q^{100}) \)

Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_0(9))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3
9.34.a.a \(1\) \(62.085\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(15\!\cdots\!40\) \(+\) \(q-2^{33}q^{4}+1589751452540q^{7}+\cdots\)
9.34.a.b \(2\) \(62.085\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(121680\) \(0\) \(181061536500\) \(-6\!\cdots\!00\) \(-\) \(q+(60840-\beta )q^{2}+(7326116992-121680\beta )q^{4}+\cdots\)
9.34.a.c \(3\) \(62.085\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-136620\) \(0\) \(260488036134\) \(10\!\cdots\!32\) \(-\) \(q+(-45540+\beta _{1})q^{2}+(4863185200+\cdots)q^{4}+\cdots\)
9.34.a.d \(3\) \(62.085\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-41202\) \(0\) \(-51261823890\) \(76\!\cdots\!56\) \(-\) \(q+(-13734+\beta _{1})q^{2}+(-369155924+\cdots)q^{4}+\cdots\)
9.34.a.e \(4\) \(62.085\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(0\) \(0\) \(-1\!\cdots\!40\) \(+\) \(q+\beta _{1}q^{2}+(8522196688+\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{34}^{\mathrm{old}}(\Gamma_0(9))\) into lower level spaces

\( S_{34}^{\mathrm{old}}(\Gamma_0(9)) \cong \) \(S_{34}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)