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Properties

Label 49.10
Level 49
Weight 10
Dimension 822
Nonzero newspaces 4
Newform subspaces 17
Sturm bound 1960
Trace bound 1

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Defining parameters

Level: \( N \) = \( 49 = 7^{2} \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 17 \)
Sturm bound: \(1960\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(49))\).

Total New Old
Modular forms 912 871 41
Cusp forms 852 822 30
Eisenstein series 60 49 11

Trace form

\( 822 q - 15 q^{2} - 339 q^{3} - 15 q^{4} - 1719 q^{5} + 15543 q^{6} - 1386 q^{7} - 101925 q^{8} + 101373 q^{9} + O(q^{10}) \) \( 822 q - 15 q^{2} - 339 q^{3} - 15 q^{4} - 1719 q^{5} + 15543 q^{6} - 1386 q^{7} - 101925 q^{8} + 101373 q^{9} + 100335 q^{10} - 148191 q^{11} - 162729 q^{12} + 731955 q^{13} - 25326 q^{14} - 89163 q^{15} - 1608567 q^{16} - 1754931 q^{17} + 1908165 q^{18} + 1437369 q^{19} + 3597867 q^{20} + 1149666 q^{21} + 3463665 q^{22} - 10605267 q^{23} - 20602809 q^{24} - 7701723 q^{25} + 17466435 q^{26} + 41156559 q^{27} + 16929318 q^{28} - 18741507 q^{29} - 65414049 q^{30} - 49031895 q^{31} - 40486035 q^{32} + 68422413 q^{33} + 138276015 q^{34} + 34642146 q^{35} - 151634169 q^{36} - 52719675 q^{37} - 136851333 q^{38} - 82217667 q^{39} - 194297877 q^{40} + 106922487 q^{41} + 271382181 q^{42} + 55775229 q^{43} + 102903267 q^{44} - 78773421 q^{45} - 310261617 q^{46} - 42610215 q^{47} - 423197478 q^{48} - 368214084 q^{49} - 130221750 q^{50} + 34430661 q^{51} + 846164403 q^{52} + 379630845 q^{53} + 966803079 q^{54} + 646715325 q^{55} - 663558756 q^{56} - 311758059 q^{57} - 965075001 q^{58} - 447530919 q^{59} + 252903315 q^{60} + 779914845 q^{61} + 280216443 q^{62} - 417625320 q^{63} - 1134480297 q^{64} + 687619191 q^{65} + 1855998015 q^{66} + 1247609985 q^{67} - 1882788537 q^{68} - 2772677793 q^{69} - 358585647 q^{70} + 1371455385 q^{71} + 3678039405 q^{72} + 2028395037 q^{73} + 190734795 q^{74} - 1846394817 q^{75} - 4225654713 q^{76} - 1818829152 q^{77} - 1970470887 q^{78} + 2037885933 q^{79} + 2286631260 q^{80} + 7316023071 q^{81} + 7567810488 q^{82} + 1804161555 q^{83} - 11327969898 q^{84} - 4578039183 q^{85} - 4459116846 q^{86} - 2354038665 q^{87} + 1036719324 q^{88} - 1551222663 q^{89} + 19228857738 q^{90} + 5117686707 q^{91} + 9723420978 q^{92} + 4909387041 q^{93} - 4493958024 q^{94} - 3688032783 q^{95} - 21565252254 q^{96} - 4615571394 q^{97} - 22074309852 q^{98} - 5220694956 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(49))\)

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
49.10.a \(\chi_{49}(1, \cdot)\) 49.10.a.a 1 1
49.10.a.b 2
49.10.a.c 3
49.10.a.d 4
49.10.a.e 5
49.10.a.f 5
49.10.a.g 8
49.10.c \(\chi_{49}(18, \cdot)\) 49.10.c.a 2 2
49.10.c.b 4
49.10.c.c 4
49.10.c.d 6
49.10.c.e 6
49.10.c.f 8
49.10.c.g 10
49.10.c.h 16
49.10.e \(\chi_{49}(8, \cdot)\) 49.10.e.a 246 6
49.10.g \(\chi_{49}(2, \cdot)\) 49.10.g.a 492 12

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(49))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(49)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 1}\)