Properties

Label 3997.1
Level 3997
Weight 1
Dimension 292
Nonzero newspaces 7
Newform subspaces 9
Sturm bound 1304160
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3997 = 7 \cdot 571 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 9 \)
Sturm bound: \(1304160\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3997))\).

Total New Old
Modular forms 3716 3136 580
Cusp forms 296 292 4
Eisenstein series 3420 2844 576

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 284 4 4 0

Trace form

\( 292 q - 2 q^{2} - 3 q^{4} + 3 q^{7} - 4 q^{8} - 3 q^{9} + O(q^{10}) \) \( 292 q - 2 q^{2} - 3 q^{4} + 3 q^{7} - 4 q^{8} - 3 q^{9} - 2 q^{11} - 4 q^{14} - 4 q^{15} - q^{16} - 4 q^{18} - 2 q^{21} - 12 q^{22} - 6 q^{23} + q^{25} - 3 q^{28} - 2 q^{29} - 2 q^{30} - 6 q^{32} - 2 q^{35} - 3 q^{36} - 2 q^{39} - 4 q^{42} - 6 q^{43} - 6 q^{44} - 2 q^{46} - q^{49} - 6 q^{50} - 4 q^{51} + 2 q^{53} - 8 q^{56} - 2 q^{57} - 8 q^{58} - 3 q^{63} + q^{64} + 4 q^{65} - 6 q^{67} + 2 q^{70} - 2 q^{72} - 6 q^{74} + 2 q^{78} + 2 q^{79} - q^{81} - 2 q^{85} - 4 q^{86} - 12 q^{88} + 2 q^{91} - 6 q^{92} - 4 q^{93} + 4 q^{95} - 6 q^{98} - 6 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3997))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3997.1.b \(\chi_{3997}(2283, \cdot)\) None 0 1
3997.1.d \(\chi_{3997}(1714, \cdot)\) None 0 1
3997.1.j \(\chi_{3997}(681, \cdot)\) None 0 2
3997.1.l \(\chi_{3997}(572, \cdot)\) None 0 2
3997.1.m \(\chi_{3997}(1032, \cdot)\) None 0 2
3997.1.n \(\chi_{3997}(461, \cdot)\) 3997.1.n.a 2 2
3997.1.n.b 4
3997.1.n.c 4
3997.1.r \(\chi_{3997}(2746, \cdot)\) None 0 2
3997.1.s \(\chi_{3997}(1604, \cdot)\) None 0 2
3997.1.t \(\chi_{3997}(1712, \cdot)\) None 0 2
3997.1.u \(\chi_{3997}(2964, \cdot)\) None 0 2
3997.1.w \(\chi_{3997}(2178, \cdot)\) None 0 4
3997.1.x \(\chi_{3997}(167, \cdot)\) 3997.1.x.a 4 4
3997.1.be \(\chi_{3997}(240, \cdot)\) None 0 8
3997.1.bf \(\chi_{3997}(468, \cdot)\) 3997.1.bf.a 8 8
3997.1.bg \(\chi_{3997}(255, \cdot)\) None 0 8
3997.1.bh \(\chi_{3997}(481, \cdot)\) None 0 8
3997.1.bi \(\chi_{3997}(184, \cdot)\) None 0 8
3997.1.bj \(\chi_{3997}(71, \cdot)\) None 0 8
3997.1.bk \(\chi_{3997}(669, \cdot)\) None 0 8
3997.1.bo \(\chi_{3997}(500, \cdot)\) None 0 8
3997.1.bp \(\chi_{3997}(55, \cdot)\) 3997.1.bp.a 18 18
3997.1.br \(\chi_{3997}(8, \cdot)\) None 0 18
3997.1.bx \(\chi_{3997}(150, \cdot)\) None 0 36
3997.1.by \(\chi_{3997}(221, \cdot)\) None 0 36
3997.1.bz \(\chi_{3997}(85, \cdot)\) None 0 36
3997.1.ca \(\chi_{3997}(58, \cdot)\) None 0 36
3997.1.ce \(\chi_{3997}(258, \cdot)\) 3997.1.ce.a 36 36
3997.1.cf \(\chi_{3997}(82, \cdot)\) None 0 36
3997.1.cg \(\chi_{3997}(31, \cdot)\) None 0 36
3997.1.ci \(\chi_{3997}(2, \cdot)\) None 0 36
3997.1.cj \(\chi_{3997}(6, \cdot)\) 3997.1.cj.a 72 72
3997.1.ck \(\chi_{3997}(15, \cdot)\) None 0 72
3997.1.cq \(\chi_{3997}(5, \cdot)\) None 0 144
3997.1.cu \(\chi_{3997}(39, \cdot)\) None 0 144
3997.1.cv \(\chi_{3997}(113, \cdot)\) None 0 144
3997.1.cw \(\chi_{3997}(86, \cdot)\) None 0 144
3997.1.cx \(\chi_{3997}(38, \cdot)\) None 0 144
3997.1.cy \(\chi_{3997}(52, \cdot)\) None 0 144
3997.1.cz \(\chi_{3997}(13, \cdot)\) 3997.1.cz.a 144 144
3997.1.da \(\chi_{3997}(18, \cdot)\) None 0 144

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3997))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3997)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(571))\)\(^{\oplus 2}\)