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Properties

Label 484.2
Level 484
Weight 2
Dimension 4025
Nonzero newspaces 8
Newform subspaces 32
Sturm bound 29040
Trace bound 1

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Defining parameters

Level: \( N \) = \( 484 = 2^{2} \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 32 \)
Sturm bound: \(29040\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(484))\).

Total New Old
Modular forms 7660 4305 3355
Cusp forms 6861 4025 2836
Eisenstein series 799 280 519

Trace form

\( 4025 q - 45 q^{2} - 45 q^{4} - 90 q^{5} - 45 q^{6} + 10 q^{7} - 45 q^{8} - 70 q^{9} + O(q^{10}) \) \( 4025 q - 45 q^{2} - 45 q^{4} - 90 q^{5} - 45 q^{6} + 10 q^{7} - 45 q^{8} - 70 q^{9} - 55 q^{10} + 5 q^{11} - 85 q^{12} - 80 q^{13} - 55 q^{14} - 85 q^{16} - 100 q^{17} - 95 q^{18} - 30 q^{19} - 95 q^{20} - 150 q^{21} - 80 q^{22} - 10 q^{23} - 105 q^{24} - 110 q^{25} - 95 q^{26} - 95 q^{28} - 80 q^{29} - 55 q^{30} - 55 q^{32} - 90 q^{33} - 45 q^{34} + 30 q^{35} + 5 q^{36} - 150 q^{37} + 5 q^{38} - 10 q^{39} + 25 q^{40} - 120 q^{41} + 45 q^{42} + 20 q^{43} - 15 q^{44} - 270 q^{45} + 5 q^{46} + 10 q^{47} + 65 q^{48} - 100 q^{49} - 25 q^{50} - 10 q^{51} - 35 q^{52} - 180 q^{53} - 55 q^{54} - 10 q^{55} - 145 q^{56} - 160 q^{57} - 115 q^{58} - 40 q^{59} - 135 q^{60} - 80 q^{61} - 195 q^{62} - 165 q^{64} - 130 q^{65} - 115 q^{66} - 30 q^{67} - 175 q^{68} - 160 q^{69} - 95 q^{70} - 40 q^{71} - 145 q^{72} - 80 q^{73} - 135 q^{74} + 10 q^{75} - 55 q^{76} - 115 q^{77} - 65 q^{78} - 10 q^{79} - 15 q^{80} + 15 q^{82} + 50 q^{83} - 35 q^{84} + 40 q^{85} + 55 q^{86} + 100 q^{87} + 30 q^{88} - 80 q^{89} + 45 q^{90} + 70 q^{91} - 55 q^{92} - 30 q^{93} + 5 q^{94} + 50 q^{95} - 55 q^{96} - 70 q^{97} - 55 q^{98} - 10 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(484))\)

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
484.2.a \(\chi_{484}(1, \cdot)\) 484.2.a.a 1 1
484.2.a.b 2
484.2.a.c 2
484.2.a.d 2
484.2.a.e 2
484.2.c \(\chi_{484}(483, \cdot)\) 484.2.c.a 2 1
484.2.c.b 4
484.2.c.c 8
484.2.c.d 16
484.2.c.e 16
484.2.e \(\chi_{484}(9, \cdot)\) 484.2.e.a 4 4
484.2.e.b 4
484.2.e.c 4
484.2.e.d 4
484.2.e.e 4
484.2.e.f 8
484.2.e.g 8
484.2.g \(\chi_{484}(215, \cdot)\) 484.2.g.a 8 4
484.2.g.b 8
484.2.g.c 8
484.2.g.d 8
484.2.g.e 8
484.2.g.f 16
484.2.g.g 16
484.2.g.h 16
484.2.g.i 16
484.2.g.j 16
484.2.g.k 64
484.2.i \(\chi_{484}(45, \cdot)\) 484.2.i.a 110 10
484.2.j \(\chi_{484}(43, \cdot)\) 484.2.j.a 640 10
484.2.m \(\chi_{484}(5, \cdot)\) 484.2.m.a 440 40
484.2.p \(\chi_{484}(7, \cdot)\) 484.2.p.a 2560 40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(484))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(484)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 2}\)