Properties

Label 3136.1
Level 3136
Weight 1
Dimension 115
Nonzero newspaces 14
Newform subspaces 19
Sturm bound 602112
Trace bound 57

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Defining parameters

Level: \( N \) = \( 3136 = 2^{6} \cdot 7^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 14 \)
Newform subspaces: \( 19 \)
Sturm bound: \(602112\)
Trace bound: \(57\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3136))\).

Total New Old
Modular forms 4728 1182 3546
Cusp forms 408 115 293
Eisenstein series 4320 1067 3253

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 107 8 0 0

Trace form

\( 115 q - 2 q^{5} + O(q^{10}) \) \( 115 q - 2 q^{5} - 2 q^{11} + 2 q^{17} + 8 q^{22} + 8 q^{29} + 2 q^{33} + 4 q^{37} + 2 q^{43} + 8 q^{44} + 16 q^{57} + 2 q^{61} + 10 q^{67} + 4 q^{69} - 2 q^{73} - 8 q^{74} + 4 q^{85} - 2 q^{89} - 2 q^{93} + 10 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3136))\)

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
3136.1.c \(\chi_{3136}(1665, \cdot)\) 3136.1.c.a 4 1
3136.1.d \(\chi_{3136}(1471, \cdot)\) 3136.1.d.a 1 1
3136.1.d.b 2
3136.1.d.c 2
3136.1.d.d 2
3136.1.g \(\chi_{3136}(3039, \cdot)\) 3136.1.g.a 4 1
3136.1.h \(\chi_{3136}(97, \cdot)\) 3136.1.h.a 8 1
3136.1.k \(\chi_{3136}(687, \cdot)\) 3136.1.k.a 2 2
3136.1.l \(\chi_{3136}(881, \cdot)\) None 0 2
3136.1.n \(\chi_{3136}(1697, \cdot)\) 3136.1.n.a 16 2
3136.1.o \(\chi_{3136}(863, \cdot)\) 3136.1.o.a 8 2
3136.1.r \(\chi_{3136}(2431, \cdot)\) 3136.1.r.a 2 2
3136.1.r.b 4
3136.1.r.c 4
3136.1.s \(\chi_{3136}(129, \cdot)\) 3136.1.s.a 8 2
3136.1.w \(\chi_{3136}(489, \cdot)\) None 0 4
3136.1.x \(\chi_{3136}(295, \cdot)\) None 0 4
3136.1.z \(\chi_{3136}(79, \cdot)\) 3136.1.z.a 4 4
3136.1.bc \(\chi_{3136}(913, \cdot)\) 3136.1.bc.a 4 4
3136.1.bd \(\chi_{3136}(545, \cdot)\) None 0 6
3136.1.be \(\chi_{3136}(351, \cdot)\) None 0 6
3136.1.bh \(\chi_{3136}(127, \cdot)\) None 0 6
3136.1.bi \(\chi_{3136}(321, \cdot)\) None 0 6
3136.1.bm \(\chi_{3136}(99, \cdot)\) 3136.1.bm.a 8 8
3136.1.bn \(\chi_{3136}(293, \cdot)\) None 0 8
3136.1.bp \(\chi_{3136}(313, \cdot)\) None 0 8
3136.1.bs \(\chi_{3136}(263, \cdot)\) None 0 8
3136.1.bu \(\chi_{3136}(209, \cdot)\) None 0 12
3136.1.bv \(\chi_{3136}(15, \cdot)\) None 0 12
3136.1.by \(\chi_{3136}(257, \cdot)\) None 0 12
3136.1.bz \(\chi_{3136}(191, \cdot)\) None 0 12
3136.1.cc \(\chi_{3136}(95, \cdot)\) None 0 12
3136.1.cd \(\chi_{3136}(33, \cdot)\) None 0 12
3136.1.ce \(\chi_{3136}(117, \cdot)\) 3136.1.ce.a 16 16
3136.1.cf \(\chi_{3136}(67, \cdot)\) 3136.1.cf.a 16 16
3136.1.cj \(\chi_{3136}(71, \cdot)\) None 0 24
3136.1.ck \(\chi_{3136}(41, \cdot)\) None 0 24
3136.1.cm \(\chi_{3136}(17, \cdot)\) None 0 24
3136.1.cp \(\chi_{3136}(207, \cdot)\) None 0 24
3136.1.cs \(\chi_{3136}(13, \cdot)\) None 0 48
3136.1.ct \(\chi_{3136}(43, \cdot)\) None 0 48
3136.1.cu \(\chi_{3136}(23, \cdot)\) None 0 48
3136.1.cx \(\chi_{3136}(73, \cdot)\) None 0 48
3136.1.cy \(\chi_{3136}(11, \cdot)\) None 0 96
3136.1.cz \(\chi_{3136}(5, \cdot)\) None 0 96

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3136))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3136)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(784))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1568))\)\(^{\oplus 2}\)