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Properties

Label 25.33
Level 25
Weight 33
Dimension 726
Nonzero newspaces 2
Sturm bound 1650
Trace bound 1

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Defining parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 33 \)
Nonzero newspaces: \( 2 \)
Sturm bound: \(1650\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{33}(\Gamma_1(25))\).

Total New Old
Modular forms 814 746 68
Cusp forms 786 726 60
Eisenstein series 28 20 8

Trace form

\( 726 q - 6 q^{2} + 5584454 q^{3} - 10 q^{4} - 229266409910 q^{5} + 1290952902462 q^{6} - 43615380273706 q^{7} - 681537872074450 q^{8} - 10 q^{9} + O(q^{10}) \) \( 726 q - 6 q^{2} + 5584454 q^{3} - 10 q^{4} - 229266409910 q^{5} + 1290952902462 q^{6} - 43615380273706 q^{7} - 681537872074450 q^{8} - 10 q^{9} + 17555754485145440 q^{10} + 121816725675067262 q^{11} - 889132547261739226 q^{12} - 1299518374046214286 q^{13} - 10 q^{14} - 6285624407445962410 q^{15} + 166004790212779250686 q^{16} + 245107631138654979144 q^{17} - 480814936319768407726 q^{18} - 1036689665254745765910 q^{19} - 1334010768656027658670 q^{20} - 2837000357984881467078 q^{21} + 8105138105706935072278 q^{22} - 22665490031029968864726 q^{23} - 44719123629362685206290 q^{25} + 52096676178849682394812 q^{26} - 326906420741816699074780 q^{27} - 403493478411032961401434 q^{28} + 268927605085096533255890 q^{29} - 2347626699605082074831050 q^{30} + 3364754418180418340622322 q^{31} - 6245035553712301715182746 q^{32} - 2281176407626351364041102 q^{33} + 26572641509683254788095990 q^{34} + 11837870627812074679460080 q^{35} - 95729599252366730908166794 q^{36} - 51603270159810028496808406 q^{37} + 18185532584447675238706280 q^{38} + 303327771564373060330566390 q^{39} - 307129184465262846364699060 q^{40} + 211650818049019693393911422 q^{41} - 634759529617240637431777182 q^{42} + 639099705490991314736240294 q^{43} + 447653938395728037086344340 q^{44} - 166441611344294008167345140 q^{45} + 4163008162300518855778092642 q^{46} - 2127866674267940213985669306 q^{47} - 4639759968958424777360258216 q^{48} + 10498339300993573346863133650 q^{50} - 5099561440560505453185675868 q^{51} + 2940573901415212720187433424 q^{52} + 34928490573397326197043594954 q^{53} - 97720940918360931511319811660 q^{54} + 35604960669174085363761555950 q^{55} + 107149594039627161591056157290 q^{56} - 218486262705492644758399342250 q^{57} + 242703679474819346922379160600 q^{58} - 12522118157898647109394685260 q^{59} + 374732756634948101006260671650 q^{60} - 74092082865006039040648235518 q^{61} - 35969145837314202660564242012 q^{62} - 108213496572455392517919536876 q^{63} + 410553658475563827961175364340 q^{64} + 651477715783194112233584017210 q^{65} - 1935330442392994047626516322066 q^{66} + 581583737812977629839009676094 q^{67} - 191575022490269548597704286034 q^{68} + 816871090131494758205589744340 q^{69} - 2882012220383063909247059406290 q^{70} - 573548879199113836701627730618 q^{71} + 7066900904959083687807079288440 q^{72} - 2151446220332151360841407676926 q^{73} + 8813913928590845157124920869910 q^{75} + 7523673076132369461414315489540 q^{76} - 22761176443204123384943955498122 q^{77} + 37030344587342122255949046534748 q^{78} + 3199693386161144759115323411790 q^{79} - 52583399316718078651389185422250 q^{80} + 45751948982634089279907733345766 q^{81} - 20998846526016374342076734718882 q^{82} - 54691759363658147385025585710216 q^{83} + 27250141253905888338653130749990 q^{84} - 14158291182852410207247936965700 q^{85} - 47823764111934701165649470301478 q^{86} - 65863374843741057805840298368620 q^{87} + 64537841459336552230466214561310 q^{88} - 2474138109146247028543837968760 q^{89} + 93077567349530641306521240801230 q^{90} - 47625471909712870591367696122038 q^{91} + 510535833659371320057277834000194 q^{92} + 168180098358789264836178299772808 q^{93} - 559481310294996557309536728527210 q^{94} - 9826647597496611607431699280690 q^{95} - 235525072934335084114136525308038 q^{96} + 410638782945815929522255760459994 q^{97} - 1275207843247479328695264727081354 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{33}^{\mathrm{new}}(\Gamma_1(25))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
25.33.c \(\chi_{25}(7, \cdot)\) 25.33.c.a 20 2
25.33.c.b 30
25.33.c.c 44
25.33.f \(\chi_{25}(2, \cdot)\) n/a 632 8

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{33}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces

\( S_{33}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{33}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)