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Properties

Label 76.15
Level 76
Weight 15
Dimension 1440
Nonzero newspaces 6
Sturm bound 5400
Trace bound 1

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Defining parameters

Level: \( N \) = \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) = \( 15 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(5400\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(\Gamma_1(76))\).

Total New Old
Modular forms 2565 1472 1093
Cusp forms 2475 1440 1035
Eisenstein series 90 32 58

Trace form

\( 1440 q + 175 q^{2} + 2775 q^{4} - 16138 q^{5} - 101577 q^{6} - 892553 q^{8} + 5997378 q^{9} + O(q^{10}) \) \( 1440 q + 175 q^{2} + 2775 q^{4} - 16138 q^{5} - 101577 q^{6} - 892553 q^{8} + 5997378 q^{9} - 11593689 q^{10} - 387849 q^{12} - 117826446 q^{13} - 350464137 q^{14} - 564941466 q^{15} + 706026999 q^{16} + 1134870431 q^{17} - 3198804762 q^{18} - 4331808957 q^{19} + 10094686382 q^{20} + 6273135375 q^{21} - 19833971529 q^{22} - 7370427285 q^{23} + 48184353783 q^{24} + 22580853036 q^{25} - 79098934105 q^{26} + 1923407118 q^{27} - 48894972 q^{28} + 80504918726 q^{29} - 108969400470 q^{30} - 104915907828 q^{31} + 133287997510 q^{32} + 487862649606 q^{33} + 5228662932 q^{34} - 274734820152 q^{35} - 1030214701059 q^{36} - 62668236828 q^{37} + 1229692066434 q^{38} + 934227370548 q^{39} - 1222641713340 q^{40} - 722905400050 q^{41} - 676324947039 q^{42} + 1509753396567 q^{43} + 711820308786 q^{44} + 3232892250831 q^{45} + 842130185808 q^{46} - 3245574061593 q^{47} - 2215787344836 q^{48} + 6393976410621 q^{49} - 1111272456918 q^{50} - 3814393506309 q^{51} - 2114318237001 q^{52} + 1235790955106 q^{53} - 890900670024 q^{54} + 6001694598276 q^{55} + 1120446093294 q^{56} - 6698723528223 q^{57} - 8967554764386 q^{58} - 5651097467535 q^{59} + 9052816012422 q^{60} - 3009580227570 q^{61} + 9798581397156 q^{62} + 7589288276100 q^{63} - 21760430495601 q^{64} - 17987797751483 q^{65} + 24105540533919 q^{66} - 6927211524687 q^{67} + 28738461509072 q^{68} + 84707684189007 q^{69} - 124967485158909 q^{70} - 17236777905477 q^{71} + 109166891234460 q^{72} - 83266285567563 q^{73} + 77154900030095 q^{74} - 130452655752099 q^{76} + 133068877905129 q^{77} - 64654798788303 q^{78} + 68922604799286 q^{79} + 13388570126351 q^{80} - 147143206833984 q^{81} + 411726375802674 q^{82} + 39469050318033 q^{83} - 519081338069589 q^{84} + 393151244432226 q^{85} + 50285131518990 q^{86} - 312316719333624 q^{87} + 315150494503887 q^{88} - 251025775303 q^{89} + 53229084568926 q^{90} + 391830115387020 q^{91} - 415905983588454 q^{92} - 953949576650622 q^{93} - 305757490726254 q^{94} + 338858637652485 q^{95} - 771793542432474 q^{96} + 173587728749685 q^{97} + 431057357252302 q^{98} + 1108758867795306 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{15}^{\mathrm{new}}(\Gamma_1(76))\)

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
76.15.b \(\chi_{76}(39, \cdot)\) n/a 126 1
76.15.c \(\chi_{76}(37, \cdot)\) 76.15.c.a 2 1
76.15.c.b 22
76.15.g \(\chi_{76}(7, \cdot)\) n/a 276 2
76.15.h \(\chi_{76}(65, \cdot)\) 76.15.h.a 48 2
76.15.j \(\chi_{76}(13, \cdot)\) n/a 138 6
76.15.l \(\chi_{76}(23, \cdot)\) n/a 828 6

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

Decomposition of \(S_{15}^{\mathrm{old}}(\Gamma_1(76))\) into lower level spaces

\( S_{15}^{\mathrm{old}}(\Gamma_1(76)) \cong \) \(S_{15}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)