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Properties

Label 25.35
Level 25
Weight 35
Dimension 772
Nonzero newspaces 2
Sturm bound 1750
Trace bound 1

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Defining parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 35 \)
Nonzero newspaces: \( 2 \)
Sturm bound: \(1750\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{35}(\Gamma_1(25))\).

Total New Old
Modular forms 864 792 72
Cusp forms 836 772 64
Eisenstein series 28 20 8

Trace form

\( 772 q - 262150 q^{2} + 157976510 q^{3} - 10 q^{4} + 730721770850 q^{5} + 88086099919614 q^{6} - 10675908470210 q^{7} + 9072239646472430 q^{8} - 10 q^{9} + O(q^{10}) \) \( 772 q - 262150 q^{2} + 157976510 q^{3} - 10 q^{4} + 730721770850 q^{5} + 88086099919614 q^{6} - 10675908470210 q^{7} + 9072239646472430 q^{8} - 10 q^{9} - 141196165961877600 q^{10} - 731963204975243106 q^{11} + 10627757137023951110 q^{12} + 22000795937426689030 q^{13} - 10 q^{14} - 208604390017026786790 q^{15} + 4092596275505244514302 q^{16} - 665304009255415083360 q^{17} + 14303545973632781542610 q^{18} + 28861225637417344972690 q^{19} - 28154981923384597962590 q^{20} + 153509466726225895805634 q^{21} + 83718472128189195521590 q^{22} + 637784720660352401849770 q^{23} - 353107743639513686653140 q^{25} + 9632612333271619541857084 q^{26} - 9404723098652687469331120 q^{27} - 29885546504778316153641210 q^{28} + 19751530910240202139799290 q^{29} - 102199380159476397875707930 q^{30} - 75177858415849500403525206 q^{31} + 31452093863850969452906470 q^{32} + 119025757551617632362479450 q^{33} + 413471259694842842693631990 q^{34} + 122560532093206690196654040 q^{35} - 3422021422235176556013479818 q^{36} - 747255640203843215021361710 q^{37} + 1124705650129417813376987480 q^{38} + 1766320610423450014949894790 q^{39} + 14252465817509015831897294540 q^{40} - 15810175913487952423757566466 q^{41} + 47077826589672703246047710370 q^{42} - 50164211911986264375336556370 q^{43} + 53589472354097078260807461940 q^{44} - 67072263917026901508904676870 q^{45} - 101315204710173754526140460606 q^{46} + 177827785687057856900055630190 q^{47} - 80766761994414191335279584680 q^{48} - 155830188603416218328199659950 q^{50} - 854842122255482942873983338436 q^{51} + 1314942404174068703566538240880 q^{52} - 1605760472796474621613307967070 q^{53} + 3672921240616866829657609427940 q^{54} - 1052473939114899628147189276130 q^{55} - 1626716753986078273144801806550 q^{56} + 4849196106069516988236395088310 q^{57} - 9885920094851373692971873067800 q^{58} + 14381094830000428606331900788240 q^{59} - 13162446668331453080358672154990 q^{60} - 3648004103246318824453425493366 q^{61} - 30895768595760809447197211363820 q^{62} + 43738092618252356583912108382360 q^{63} - 28002650369425458689529124122060 q^{64} + 80406610560207004283574030066180 q^{65} - 16312458793293745366879556259282 q^{66} - 9818513294447748970668126351450 q^{67} + 54023829585520936773191222387630 q^{68} - 132699393143611812708489865605560 q^{69} + 112504576231296861534113012694270 q^{70} + 297559066981533221529260004600774 q^{71} - 1308046088663282892588649263900600 q^{72} + 784821994838560295820563631971790 q^{73} - 896465790447266668356490014014790 q^{75} + 1780161826572616274040532125572420 q^{76} - 174065550949024199929478569806250 q^{77} - 2198754985480590928526905557350900 q^{78} + 226853868573322161712843838318590 q^{79} + 3134077731566217922673059501893110 q^{80} - 120620357215236458767057353390598 q^{81} - 2017337332967969119350086593701250 q^{82} + 1871565792897549506111407464153780 q^{83} + 1612159429950188923416707871149990 q^{84} - 8214101745096066387645425232460240 q^{85} + 7663919988796819910260127198249274 q^{86} - 9279637121322379543108970627332560 q^{87} + 7721869906656633379656736945592670 q^{88} + 3876220850390318848705348446937490 q^{89} - 23043983836208396429751995054212450 q^{90} - 1011977834185573578095559140001326 q^{91} + 30826748156198036191247659338571650 q^{92} - 32453135565280004188416076697518940 q^{93} + 31563998364364720905605416394461590 q^{94} + 22373742305000135111528774031032710 q^{95} - 93362874340629498928493523414456486 q^{96} + 32397591527679001813213600449150990 q^{97} + 49001159728803321679651258037893430 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{35}^{\mathrm{new}}(\Gamma_1(25))\)

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
25.35.c \(\chi_{25}(7, \cdot)\) 25.35.c.a 24 2
25.35.c.b 32
25.35.c.c 44
25.35.f \(\chi_{25}(2, \cdot)\) n/a 672 8

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

Decomposition of \(S_{35}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces

\( S_{35}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{35}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{35}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{35}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 1}\)