Properties

Label 348.2
Level 348
Weight 2
Dimension 1414
Nonzero newspaces 12
Newform subspaces 22
Sturm bound 13440
Trace bound 6

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Defining parameters

Level: \( N \) = \( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 22 \)
Sturm bound: \(13440\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(348))\).

Total New Old
Modular forms 3640 1518 2122
Cusp forms 3081 1414 1667
Eisenstein series 559 104 455

Trace form

\( 1414q - 28q^{4} - 14q^{6} - 28q^{9} + O(q^{10}) \) \( 1414q - 28q^{4} - 14q^{6} - 28q^{9} - 28q^{10} - 14q^{12} - 56q^{13} - 28q^{16} - 14q^{18} - 28q^{22} + 28q^{23} - 14q^{24} + 42q^{27} - 56q^{28} + 56q^{29} - 28q^{30} + 56q^{31} + 14q^{33} - 28q^{34} + 56q^{35} - 14q^{36} - 28q^{37} + 28q^{39} - 28q^{40} - 14q^{42} - 28q^{44} - 42q^{45} - 168q^{46} - 56q^{47} - 126q^{48} - 168q^{49} - 196q^{50} - 56q^{51} - 252q^{52} - 126q^{53} - 14q^{54} - 224q^{55} - 196q^{56} - 112q^{57} - 364q^{58} - 56q^{59} - 182q^{60} - 168q^{61} - 196q^{62} - 28q^{63} - 280q^{64} - 126q^{65} - 126q^{66} - 112q^{67} - 196q^{68} - 84q^{69} - 252q^{70} - 56q^{71} - 42q^{72} - 126q^{73} - 28q^{74} - 70q^{75} - 28q^{76} - 14q^{78} - 140q^{81} - 28q^{82} + 28q^{84} - 56q^{85} - 70q^{87} - 56q^{88} - 14q^{90} - 84q^{93} - 28q^{94} + 28q^{96} - 210q^{97} + 140q^{98} - 126q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(348))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
348.2.a \(\chi_{348}(1, \cdot)\) 348.2.a.a 1 1
348.2.a.b 1
348.2.a.c 1
348.2.a.d 1
348.2.b \(\chi_{348}(347, \cdot)\) 348.2.b.a 8 1
348.2.b.b 12
348.2.b.c 12
348.2.b.d 24
348.2.c \(\chi_{348}(59, \cdot)\) 348.2.c.a 16 1
348.2.c.b 40
348.2.h \(\chi_{348}(289, \cdot)\) 348.2.h.a 2 1
348.2.h.b 2
348.2.h.c 2
348.2.i \(\chi_{348}(307, \cdot)\) 348.2.i.a 60 2
348.2.l \(\chi_{348}(17, \cdot)\) 348.2.l.a 20 2
348.2.m \(\chi_{348}(25, \cdot)\) 348.2.m.a 12 6
348.2.m.b 12
348.2.n \(\chi_{348}(13, \cdot)\) 348.2.n.a 36 6
348.2.s \(\chi_{348}(23, \cdot)\) 348.2.s.a 336 6
348.2.t \(\chi_{348}(35, \cdot)\) 348.2.t.a 336 6
348.2.u \(\chi_{348}(77, \cdot)\) 348.2.u.a 120 12
348.2.x \(\chi_{348}(19, \cdot)\) 348.2.x.a 360 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(348))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(348)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(174))\)\(^{\oplus 2}\)