Properties

Label 1.48.a
Level 1
Weight 48
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 1
Sturm bound 4
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 48 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{48}(\Gamma_0(1))\).

Total New Old
Modular forms 5 5 0
Cusp forms 4 4 0
Eisenstein series 1 1 0

Trace form

\(4q \) \(\mathstrut +\mathstrut 5785560q^{2} \) \(\mathstrut +\mathstrut 38461494960q^{3} \) \(\mathstrut +\mathstrut 404807499161152q^{4} \) \(\mathstrut -\mathstrut 31114680242272200q^{5} \) \(\mathstrut +\mathstrut 2130087053081157408q^{6} \) \(\mathstrut -\mathstrut 39169218725888423200q^{7} \) \(\mathstrut +\mathstrut 2392716988073784337920q^{8} \) \(\mathstrut -\mathstrut 17071972417358142200172q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 5785560q^{2} \) \(\mathstrut +\mathstrut 38461494960q^{3} \) \(\mathstrut +\mathstrut 404807499161152q^{4} \) \(\mathstrut -\mathstrut 31114680242272200q^{5} \) \(\mathstrut +\mathstrut 2130087053081157408q^{6} \) \(\mathstrut -\mathstrut 39169218725888423200q^{7} \) \(\mathstrut +\mathstrut 2392716988073784337920q^{8} \) \(\mathstrut -\mathstrut 17071972417358142200172q^{9} \) \(\mathstrut +\mathstrut 161126302562215963534800q^{10} \) \(\mathstrut -\mathstrut 1902165515717740404742512q^{11} \) \(\mathstrut +\mathstrut 50498409864612604588081920q^{12} \) \(\mathstrut +\mathstrut 126959149195199610466858520q^{13} \) \(\mathstrut +\mathstrut 3491363489769461659480835904q^{14} \) \(\mathstrut +\mathstrut 12437812896841241272880733600q^{15} \) \(\mathstrut +\mathstrut 124527684040554167211817897984q^{16} \) \(\mathstrut +\mathstrut 210426285758836687099688769480q^{17} \) \(\mathstrut +\mathstrut 407430960534937802050318472760q^{18} \) \(\mathstrut -\mathstrut 1059119811802437301721159140240q^{19} \) \(\mathstrut -\mathstrut 15129514318106701401937782249600q^{20} \) \(\mathstrut -\mathstrut 26054906182888686128940663165312q^{21} \) \(\mathstrut -\mathstrut 79668451994083088127806382590880q^{22} \) \(\mathstrut +\mathstrut 137531418344493639994288859179680q^{23} \) \(\mathstrut +\mathstrut 1127389844243414442148606193633280q^{24} \) \(\mathstrut +\mathstrut 1009909900344396506188154274977500q^{25} \) \(\mathstrut +\mathstrut 2282338781897562472343866220387088q^{26} \) \(\mathstrut -\mathstrut 7345952425324536073931587214783520q^{27} \) \(\mathstrut -\mathstrut 36222097928665071743339635065479680q^{28} \) \(\mathstrut -\mathstrut 22743132490172744184500850941726760q^{29} \) \(\mathstrut -\mathstrut 25720928123802268640488729686158400q^{30} \) \(\mathstrut +\mathstrut 75786540814706434901630981303934848q^{31} \) \(\mathstrut +\mathstrut 1184674767018086471839527432906178560q^{32} \) \(\mathstrut +\mathstrut 263381387470144952341649359926294720q^{33} \) \(\mathstrut -\mathstrut 1261659118578465318749852382715620816q^{34} \) \(\mathstrut -\mathstrut 1313148822925052387484546800067979200q^{35} \) \(\mathstrut -\mathstrut 13289406181678982858450254524690284736q^{36} \) \(\mathstrut -\mathstrut 11291457045120157869429951769632191560q^{37} \) \(\mathstrut +\mathstrut 29667542464851305273548614410680536480q^{38} \) \(\mathstrut +\mathstrut 39294375338503805226442587829551714336q^{39} \) \(\mathstrut +\mathstrut 70753686685508718175919216681780352000q^{40} \) \(\mathstrut +\mathstrut 130658126291089294119301677048020391528q^{41} \) \(\mathstrut -\mathstrut 109062084819684721847642948723433304320q^{42} \) \(\mathstrut -\mathstrut 445357287738427943170332944488133090800q^{43} \) \(\mathstrut -\mathstrut 1525898906718917337200010663037616115456q^{44} \) \(\mathstrut +\mathstrut 86022747271219179966948746072020632600q^{45} \) \(\mathstrut +\mathstrut 1226146172325422687186041586267533291968q^{46} \) \(\mathstrut +\mathstrut 2031912465958423919194866366997063590720q^{47} \) \(\mathstrut +\mathstrut 10099193618530117215910418995824892231680q^{48} \) \(\mathstrut +\mathstrut 9153745744156628626499502447643951451172q^{49} \) \(\mathstrut -\mathstrut 19226200465513908889722489088356697935000q^{50} \) \(\mathstrut -\mathstrut 18534366050002170683962116343746386369952q^{51} \) \(\mathstrut -\mathstrut 55272350705889116147839999778699925596800q^{52} \) \(\mathstrut +\mathstrut 29171719896619533806321793123448457437560q^{53} \) \(\mathstrut -\mathstrut 119298079293441315567989538387565460341440q^{54} \) \(\mathstrut +\mathstrut 192172580604633896452606078657416872901600q^{55} \) \(\mathstrut +\mathstrut 276101696826518177934513744689489393111040q^{56} \) \(\mathstrut +\mathstrut 558743644452458098451223285784560964733760q^{57} \) \(\mathstrut -\mathstrut 732323136683092912071778597620095648941680q^{58} \) \(\mathstrut +\mathstrut 478242858216320686410790860443879577596880q^{59} \) \(\mathstrut -\mathstrut 2122170544542769609835673200272436380915200q^{60} \) \(\mathstrut +\mathstrut 626683213833907852009669690320782900857688q^{61} \) \(\mathstrut -\mathstrut 6870459615610782098804391369236375065946880q^{62} \) \(\mathstrut +\mathstrut 5811636950821577036406237472810763671724640q^{63} \) \(\mathstrut +\mathstrut 5525430481808418303700543890989262651523072q^{64} \) \(\mathstrut +\mathstrut 12996735432890074297558542478104126872331600q^{65} \) \(\mathstrut -\mathstrut 8968962593451471455705715472787747435620224q^{66} \) \(\mathstrut +\mathstrut 18701411419127220668869505853739529194216880q^{67} \) \(\mathstrut -\mathstrut 27469024204738931095482995064729717598496640q^{68} \) \(\mathstrut -\mathstrut 2096956664577882726873494616728974107851904q^{69} \) \(\mathstrut -\mathstrut 97207317904230285933067401805385458355395200q^{70} \) \(\mathstrut +\mathstrut 22196594617762006008028198712153461686540768q^{71} \) \(\mathstrut -\mathstrut 17423883005618236773493453708136577246773760q^{72} \) \(\mathstrut +\mathstrut 104911201720506650033573412943840886878191080q^{73} \) \(\mathstrut +\mathstrut 187734656069700274526204928907842421165646544q^{74} \) \(\mathstrut +\mathstrut 32388703324174028323482311940739905891330000q^{75} \) \(\mathstrut +\mathstrut 351694386032713991264839561028061045130100480q^{76} \) \(\mathstrut -\mathstrut 263490744376507692433815778071300370399209600q^{77} \) \(\mathstrut -\mathstrut 49672827098281461020739302707360391741486400q^{78} \) \(\mathstrut -\mathstrut 1327995310109394234162785254414226288730352960q^{79} \) \(\mathstrut -\mathstrut 948349663264469859337474495994045561022259200q^{80} \) \(\mathstrut -\mathstrut 1061448205755511803861508510986654404170081116q^{81} \) \(\mathstrut +\mathstrut 3821513842864797430908620724480935919685390320q^{82} \) \(\mathstrut -\mathstrut 1439130627532364606968733068855111784504073360q^{83} \) \(\mathstrut +\mathstrut 5249451328483250861794821516342136498695481344q^{84} \) \(\mathstrut -\mathstrut 1001895286410663502447652611446390227458237200q^{85} \) \(\mathstrut +\mathstrut 9578145533777866709022895861637903827077656928q^{86} \) \(\mathstrut -\mathstrut 4326251093943206485496474339443178030108648160q^{87} \) \(\mathstrut -\mathstrut 15478856320702836436797993507832298416714229760q^{88} \) \(\mathstrut -\mathstrut 7960590522674945421108320896849737731421281880q^{89} \) \(\mathstrut -\mathstrut 16839942698767843070418568109517409659960668400q^{90} \) \(\mathstrut +\mathstrut 5325194479227227497182497798631911205603381568q^{91} \) \(\mathstrut +\mathstrut 13058297350229360275908546071900174502239009280q^{92} \) \(\mathstrut +\mathstrut 10728611999875738337226031496188630272675064320q^{93} \) \(\mathstrut +\mathstrut 3475860200879106349192555645858186353201354624q^{94} \) \(\mathstrut +\mathstrut 75421152415106939771624998522249518123547668000q^{95} \) \(\mathstrut +\mathstrut 64914496577750590120454418039013206176753123328q^{96} \) \(\mathstrut +\mathstrut 95066248961258904822565865801364599382905757320q^{97} \) \(\mathstrut -\mathstrut 296344663186266398350742083591017164797938217320q^{98} \) \(\mathstrut +\mathstrut 530900415919166351015781326273177630089784016q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{48}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.48.a.a \(4\) \(13.991\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(5785560\) \(38461494960\) \(-3\!\cdots\!00\) \(-3\!\cdots\!00\) \(+\) \(q+(1446390+\beta _{1})q^{2}+(9615373740+\cdots)q^{3}+\cdots\)