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Properties

Label 328.2
Level 328
Weight 2
Dimension 1810
Nonzero newspaces 14
Newform subspaces 31
Sturm bound 13440
Trace bound 6

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Defining parameters

Level: \( N \) = \( 328 = 2^{3} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 14 \)
Newform subspaces: \( 31 \)
Sturm bound: \(13440\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(328))\).

Total New Old
Modular forms 3600 1966 1634
Cusp forms 3121 1810 1311
Eisenstein series 479 156 323

Trace form

\( 1810 q - 40 q^{2} - 40 q^{3} - 40 q^{4} - 40 q^{6} - 40 q^{7} - 40 q^{8} - 80 q^{9} + O(q^{10}) \) \( 1810 q - 40 q^{2} - 40 q^{3} - 40 q^{4} - 40 q^{6} - 40 q^{7} - 40 q^{8} - 80 q^{9} - 40 q^{10} - 40 q^{11} - 40 q^{12} - 40 q^{14} - 40 q^{15} - 40 q^{16} - 80 q^{17} - 40 q^{18} - 40 q^{19} - 40 q^{20} - 40 q^{22} - 40 q^{23} - 40 q^{24} - 80 q^{25} - 40 q^{26} - 40 q^{27} - 40 q^{28} - 40 q^{30} - 40 q^{31} - 40 q^{32} - 80 q^{33} - 40 q^{34} - 40 q^{35} - 40 q^{36} - 40 q^{38} - 40 q^{39} - 40 q^{40} - 80 q^{41} - 80 q^{42} - 40 q^{43} - 40 q^{44} - 40 q^{46} - 40 q^{47} - 40 q^{48} - 80 q^{49} - 40 q^{50} - 40 q^{51} - 40 q^{52} - 40 q^{54} - 40 q^{55} - 40 q^{56} - 80 q^{57} - 40 q^{58} - 40 q^{59} - 40 q^{60} - 40 q^{62} - 40 q^{63} - 40 q^{64} - 90 q^{65} - 40 q^{66} - 100 q^{67} - 40 q^{68} - 80 q^{69} - 40 q^{70} - 120 q^{71} - 40 q^{72} - 160 q^{73} - 40 q^{74} - 200 q^{75} - 40 q^{76} - 80 q^{77} - 40 q^{78} - 120 q^{79} - 40 q^{80} - 250 q^{81} - 40 q^{82} - 160 q^{83} - 40 q^{84} - 170 q^{85} - 40 q^{86} - 120 q^{87} - 40 q^{88} - 160 q^{89} - 40 q^{90} - 200 q^{91} - 40 q^{92} - 80 q^{93} - 40 q^{94} - 120 q^{95} - 40 q^{96} - 160 q^{97} - 40 q^{98} - 100 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(328))\)

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
328.2.a \(\chi_{328}(1, \cdot)\) 328.2.a.a 1 1
328.2.a.b 1
328.2.a.c 2
328.2.a.d 3
328.2.a.e 3
328.2.b \(\chi_{328}(165, \cdot)\) 328.2.b.a 20 1
328.2.b.b 20
328.2.d \(\chi_{328}(81, \cdot)\) 328.2.d.a 4 1
328.2.d.b 6
328.2.g \(\chi_{328}(245, \cdot)\) 328.2.g.a 40 1
328.2.j \(\chi_{328}(9, \cdot)\) 328.2.j.a 2 2
328.2.j.b 2
328.2.j.c 8
328.2.j.d 10
328.2.l \(\chi_{328}(173, \cdot)\) 328.2.l.a 80 2
328.2.m \(\chi_{328}(57, \cdot)\) 328.2.m.a 8 4
328.2.m.b 12
328.2.m.c 20
328.2.p \(\chi_{328}(3, \cdot)\) 328.2.p.a 4 4
328.2.p.b 4
328.2.p.c 152
328.2.q \(\chi_{328}(55, \cdot)\) None 0 4
328.2.s \(\chi_{328}(25, \cdot)\) 328.2.s.a 16 4
328.2.s.b 24
328.2.u \(\chi_{328}(37, \cdot)\) 328.2.u.a 160 4
328.2.w \(\chi_{328}(45, \cdot)\) 328.2.w.a 160 4
328.2.y \(\chi_{328}(5, \cdot)\) 328.2.y.a 320 8
328.2.ba \(\chi_{328}(33, \cdot)\) 328.2.ba.a 40 8
328.2.ba.b 48
328.2.bc \(\chi_{328}(7, \cdot)\) None 0 16
328.2.bd \(\chi_{328}(11, \cdot)\) 328.2.bd.a 16 16
328.2.bd.b 16
328.2.bd.c 608

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(328))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(328)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 2}\)