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Properties

Label 50.14
Level 50
Weight 14
Dimension 301
Nonzero newspaces 4
Sturm bound 2100
Trace bound 1

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Defining parameters

Level: \( N \) = \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) = \( 14 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(2100\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(50))\).

Total New Old
Modular forms 1003 301 702
Cusp forms 947 301 646
Eisenstein series 56 0 56

Trace form

\( 301 q + 128 q^{2} + 4192 q^{3} + 71555 q^{5} - 83456 q^{6} - 715296 q^{7} + 524288 q^{8} - 18545920 q^{9} + O(q^{10}) \) \( 301 q + 128 q^{2} + 4192 q^{3} + 71555 q^{5} - 83456 q^{6} - 715296 q^{7} + 524288 q^{8} - 18545920 q^{9} + 7201600 q^{10} - 17249408 q^{11} + 17170432 q^{12} - 13586328 q^{13} - 88622080 q^{14} - 58732420 q^{15} - 402653184 q^{16} + 558476284 q^{17} - 1242229696 q^{18} - 522935480 q^{19} + 618987520 q^{20} + 175210312 q^{21} - 3879747584 q^{22} + 3794453672 q^{23} + 3098542080 q^{24} + 2920356935 q^{25} - 1441870336 q^{26} + 4209063100 q^{27} + 407650304 q^{28} + 1696340600 q^{29} + 7359970560 q^{30} + 18847665832 q^{31} - 3221225472 q^{32} + 27542581704 q^{33} - 13894041920 q^{34} - 117171852580 q^{35} - 6153142272 q^{36} + 157047375269 q^{37} - 33498805760 q^{38} - 112726523640 q^{39} + 10906501120 q^{40} + 199506631412 q^{41} + 259792408576 q^{42} + 95898019432 q^{43} - 59616133120 q^{44} - 569783276725 q^{45} + 102336436224 q^{46} + 198582092744 q^{47} + 70330089472 q^{48} + 522273585165 q^{49} - 227633790400 q^{50} + 265813423052 q^{51} - 55649599488 q^{52} - 311022742803 q^{53} + 646435230720 q^{54} + 1178588801500 q^{55} - 382847680512 q^{56} - 517450411760 q^{57} + 1240506259200 q^{58} - 554954435620 q^{59} - 687841607680 q^{60} - 933043667748 q^{61} + 518265469696 q^{62} - 6570947671988 q^{63} + 4593369977335 q^{65} + 1897398339328 q^{66} + 2406279032624 q^{67} + 43166613504 q^{68} - 923498030580 q^{69} - 8408430848000 q^{70} - 2069972738608 q^{71} - 1605321097216 q^{72} + 17107868915672 q^{73} + 10300449914880 q^{74} + 17124525556460 q^{75} + 1600570163200 q^{76} - 12503548551872 q^{77} - 14907370354432 q^{78} - 19595256856240 q^{79} + 1200493690880 q^{80} + 14174919966296 q^{81} + 18030520852736 q^{82} + 38732435945952 q^{83} - 299587092480 q^{84} - 20092942335945 q^{85} - 13669963358976 q^{86} - 32834411687060 q^{87} + 1978606288896 q^{88} + 19592991924805 q^{89} + 59655235033920 q^{90} + 43054505792912 q^{91} - 24421734596608 q^{92} - 14583523868036 q^{93} - 60138774804480 q^{94} - 44686296470060 q^{95} - 1400159338496 q^{96} + 25278887806604 q^{97} + 35973402662016 q^{98} + 73904680150460 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(50))\)

We only show spaces with even 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
50.14.a \(\chi_{50}(1, \cdot)\) 50.14.a.a 1 1
50.14.a.b 1
50.14.a.c 1
50.14.a.d 1
50.14.a.e 1
50.14.a.f 2
50.14.a.g 2
50.14.a.h 3
50.14.a.i 3
50.14.a.j 3
50.14.a.k 3
50.14.b \(\chi_{50}(49, \cdot)\) 50.14.b.a 2 1
50.14.b.b 2
50.14.b.c 2
50.14.b.d 2
50.14.b.e 2
50.14.b.f 4
50.14.b.g 6
50.14.d \(\chi_{50}(11, \cdot)\) n/a 132 4
50.14.e \(\chi_{50}(9, \cdot)\) n/a 128 4

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

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(50))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(50)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 1}\)