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Properties

Label 49.20
Level 49
Weight 20
Dimension 1763
Nonzero newspaces 4
Sturm bound 3920
Trace bound 1

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Defining parameters

Level: \( N \) = \( 49 = 7^{2} \)
Weight: \( k \) = \( 20 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(3920\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_1(49))\).

Total New Old
Modular forms 1892 1812 80
Cusp forms 1832 1763 69
Eisenstein series 60 49 11

Trace form

\( 1763 q + 441 q^{2} + 11271 q^{3} + 1780785 q^{4} + 2608821 q^{5} - 97835049 q^{6} + 146493634 q^{7} - 1516784181 q^{8} + 2824959426 q^{9} + O(q^{10}) \) \( 1763 q + 441 q^{2} + 11271 q^{3} + 1780785 q^{4} + 2608821 q^{5} - 97835049 q^{6} + 146493634 q^{7} - 1516784181 q^{8} + 2824959426 q^{9} + 5355698559 q^{10} - 7809578721 q^{11} + 87411721383 q^{12} - 252484332555 q^{13} + 127084457010 q^{14} - 791867835711 q^{15} + 434869728585 q^{16} + 210085705593 q^{17} - 4525363472163 q^{18} + 8879770852503 q^{19} - 11790488859765 q^{20} - 4751926305105 q^{21} + 11417260486881 q^{22} - 4195279619685 q^{23} - 96735279006729 q^{24} + 188228944016520 q^{25} - 45918514160253 q^{26} - 267220783782621 q^{27} + 124858417477990 q^{28} + 200359092792843 q^{29} - 407570067282129 q^{30} - 387816560568093 q^{31} + 1986575995290717 q^{32} + 1892024293630035 q^{33} - 6518262416311041 q^{34} + 1268243427950457 q^{35} + 1238834231714007 q^{36} - 12730617341200591 q^{37} + 4176652126027851 q^{38} - 4551829213192338 q^{39} + 38195013490508859 q^{40} - 19078611142105137 q^{41} - 40582559199342531 q^{42} + 32973229064812755 q^{43} + 61773826556661411 q^{44} - 40756471041434412 q^{45} - 118346052322578705 q^{46} + 398368433257233 q^{47} + 306784774448999514 q^{48} + 43578226571218612 q^{49} - 355276483294449726 q^{50} - 69534668080582281 q^{51} + 434264677775210387 q^{52} - 19832239628668173 q^{53} - 72074638206796713 q^{54} - 417671412731928330 q^{55} - 248323514944728132 q^{56} + 186432147608017695 q^{57} + 914235076816353495 q^{58} - 334544863639962723 q^{59} - 1422644960562657405 q^{60} + 629496607546304132 q^{61} + 377517970315309659 q^{62} - 125838066898938198 q^{63} - 1959892659209912649 q^{64} - 224205923595003273 q^{65} + 139017281405002575 q^{66} + 608563737206976327 q^{67} + 851518365031171047 q^{68} - 4708713344492364645 q^{69} + 999052479547466337 q^{70} + 2043369566700941505 q^{71} - 546657382961910675 q^{72} - 1115622695399842671 q^{73} + 4013970708865001883 q^{74} + 2073483008738185719 q^{75} - 8411750964224351289 q^{76} - 2158589629318536477 q^{77} + 9960427954886848761 q^{78} - 3270220750861696653 q^{79} + 13672385702694387516 q^{80} - 4286121438344391654 q^{81} + 29012929246435666224 q^{82} - 21026153606441922309 q^{83} - 56953279824133108122 q^{84} + 11271972371151922065 q^{85} + 66105297541472363034 q^{86} + 3598456083487889115 q^{87} - 88396884925552181316 q^{88} - 42701552257350606699 q^{89} + 74765771882916069570 q^{90} + 34829620676432172353 q^{91} + 5038061315257885890 q^{92} - 23879941638859544913 q^{93} - 42335150399689346352 q^{94} - 101777642954245918077 q^{95} + 85928212258256961474 q^{96} + 70810887907919399184 q^{97} + 115086911675992203276 q^{98} - 113830992298373102328 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_1(49))\)

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
49.20.a \(\chi_{49}(1, \cdot)\) 49.20.a.a 1 1
49.20.a.b 1
49.20.a.c 4
49.20.a.d 5
49.20.a.e 8
49.20.a.f 12
49.20.a.g 12
49.20.a.h 20
49.20.c \(\chi_{49}(18, \cdot)\) n/a 122 2
49.20.e \(\chi_{49}(8, \cdot)\) n/a 522 6
49.20.g \(\chi_{49}(2, \cdot)\) n/a 1056 12

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

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_1(49))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_1(49)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)