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Properties

Label 395.3
Level 395
Weight 3
Dimension 11206
Nonzero newspaces 12
Newform subspaces 16
Sturm bound 37440
Trace bound 2

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Defining parameters

Level: \( N \) = \( 395 = 5 \cdot 79 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 16 \)
Sturm bound: \(37440\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(395))\).

Total New Old
Modular forms 12792 11666 1126
Cusp forms 12168 11206 962
Eisenstein series 624 460 164

Trace form

\( 11206 q - 78 q^{2} - 78 q^{3} - 78 q^{4} - 117 q^{5} - 234 q^{6} - 78 q^{7} - 78 q^{8} - 78 q^{9} + O(q^{10}) \) \( 11206 q - 78 q^{2} - 78 q^{3} - 78 q^{4} - 117 q^{5} - 234 q^{6} - 78 q^{7} - 78 q^{8} - 78 q^{9} - 117 q^{10} - 234 q^{11} - 78 q^{12} - 78 q^{13} - 78 q^{14} - 117 q^{15} - 234 q^{16} - 78 q^{17} - 78 q^{18} - 78 q^{19} - 117 q^{20} - 234 q^{21} - 78 q^{22} - 78 q^{23} - 78 q^{24} - 117 q^{25} - 234 q^{26} - 78 q^{27} - 78 q^{28} - 78 q^{29} - 117 q^{30} - 234 q^{31} - 78 q^{32} - 78 q^{33} - 78 q^{34} - 117 q^{35} - 234 q^{36} - 78 q^{37} - 78 q^{38} - 78 q^{39} - 117 q^{40} - 234 q^{41} - 78 q^{42} - 78 q^{43} - 78 q^{44} - 117 q^{45} - 234 q^{46} - 78 q^{47} - 78 q^{48} - 78 q^{49} - 117 q^{50} - 234 q^{51} - 78 q^{52} - 78 q^{53} - 78 q^{54} - 117 q^{55} - 234 q^{56} - 78 q^{57} - 78 q^{58} - 78 q^{59} - 117 q^{60} - 234 q^{61} - 78 q^{62} - 1638 q^{63} - 4446 q^{64} - 1131 q^{65} - 3978 q^{66} - 2080 q^{67} - 3198 q^{68} - 2886 q^{69} - 2613 q^{70} - 1326 q^{71} - 4758 q^{72} - 858 q^{73} - 1326 q^{74} - 585 q^{75} - 1690 q^{76} - 312 q^{77} - 156 q^{78} + 390 q^{79} + 546 q^{80} + 1170 q^{81} + 1170 q^{82} + 1092 q^{83} + 4290 q^{84} + 975 q^{85} + 2262 q^{86} + 1326 q^{87} + 7722 q^{88} + 1638 q^{89} + 3627 q^{90} + 3822 q^{91} + 4290 q^{92} + 2652 q^{93} + 4914 q^{94} + 1209 q^{95} + 5382 q^{96} + 1898 q^{97} - 78 q^{98} - 78 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(395))\)

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
395.3.c \(\chi_{395}(394, \cdot)\) 395.3.c.a 4 1
395.3.c.b 4
395.3.c.c 10
395.3.c.d 60
395.3.d \(\chi_{395}(236, \cdot)\) 395.3.d.a 4 1
395.3.d.b 48
395.3.g \(\chi_{395}(238, \cdot)\) 395.3.g.a 156 2
395.3.h \(\chi_{395}(56, \cdot)\) 395.3.h.a 108 2
395.3.i \(\chi_{395}(24, \cdot)\) 395.3.i.a 156 2
395.3.k \(\chi_{395}(23, \cdot)\) 395.3.k.a 312 4
395.3.n \(\chi_{395}(41, \cdot)\) 395.3.n.a 624 12
395.3.o \(\chi_{395}(14, \cdot)\) 395.3.o.a 936 12
395.3.r \(\chi_{395}(8, \cdot)\) 395.3.r.a 1872 24
395.3.u \(\chi_{395}(29, \cdot)\) 395.3.u.a 1872 24
395.3.v \(\chi_{395}(6, \cdot)\) 395.3.v.a 1296 24
395.3.x \(\chi_{395}(2, \cdot)\) 395.3.x.a 3744 48

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(395))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(395)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(79))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(395))\)\(^{\oplus 1}\)