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Properties

Label 2144.1
Level 2144
Weight 1
Dimension 42
Nonzero newspaces 5
Newform subspaces 6
Sturm bound 287232
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2144 = 2^{5} \cdot 67 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 6 \)
Sturm bound: \(287232\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2144))\).

Total New Old
Modular forms 2274 692 1582
Cusp forms 162 42 120
Eisenstein series 2112 650 1462

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 38 4 0 0

Trace form

\( 42 q + 2 q^{3} + 5 q^{9} + O(q^{10}) \) \( 42 q + 2 q^{3} + 5 q^{9} + 2 q^{11} - 2 q^{13} + 4 q^{15} - 2 q^{17} + 2 q^{19} + 2 q^{23} - q^{25} + 4 q^{27} + 2 q^{29} - 8 q^{33} - 2 q^{37} + 4 q^{39} + 2 q^{43} + 2 q^{47} + 5 q^{49} + 4 q^{51} + 4 q^{55} - 4 q^{57} + 2 q^{59} + 2 q^{61} - 4 q^{65} + q^{67} + 2 q^{71} - 2 q^{73} + 2 q^{75} + 2 q^{77} + q^{81} + 2 q^{83} - 4 q^{89} + 6 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2144))\)

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
2144.1.b \(\chi_{2144}(1473, \cdot)\) None 0 1
2144.1.d \(\chi_{2144}(671, \cdot)\) None 0 1
2144.1.f \(\chi_{2144}(1743, \cdot)\) None 0 1
2144.1.h \(\chi_{2144}(401, \cdot)\) 2144.1.h.a 3 1
2144.1.h.b 3
2144.1.l \(\chi_{2144}(135, \cdot)\) None 0 2
2144.1.m \(\chi_{2144}(937, \cdot)\) None 0 2
2144.1.o \(\chi_{2144}(97, \cdot)\) None 0 2
2144.1.q \(\chi_{2144}(1503, \cdot)\) 2144.1.q.a 4 2
2144.1.s \(\chi_{2144}(431, \cdot)\) 2144.1.s.a 2 2
2144.1.t \(\chi_{2144}(1169, \cdot)\) None 0 2
2144.1.u \(\chi_{2144}(133, \cdot)\) None 0 4
2144.1.w \(\chi_{2144}(403, \cdot)\) None 0 4
2144.1.z \(\chi_{2144}(439, \cdot)\) None 0 4
2144.1.ba \(\chi_{2144}(105, \cdot)\) None 0 4
2144.1.bd \(\chi_{2144}(177, \cdot)\) None 0 10
2144.1.bf \(\chi_{2144}(15, \cdot)\) 2144.1.bf.a 10 10
2144.1.bh \(\chi_{2144}(159, \cdot)\) None 0 10
2144.1.bj \(\chi_{2144}(161, \cdot)\) None 0 10
2144.1.bl \(\chi_{2144}(365, \cdot)\) None 0 8
2144.1.bn \(\chi_{2144}(163, \cdot)\) None 0 8
2144.1.bp \(\chi_{2144}(137, \cdot)\) None 0 20
2144.1.bq \(\chi_{2144}(215, \cdot)\) None 0 20
2144.1.bt \(\chi_{2144}(113, \cdot)\) None 0 20
2144.1.bu \(\chi_{2144}(47, \cdot)\) 2144.1.bu.a 20 20
2144.1.bw \(\chi_{2144}(127, \cdot)\) None 0 20
2144.1.by \(\chi_{2144}(353, \cdot)\) None 0 20
2144.1.cb \(\chi_{2144}(59, \cdot)\) None 0 40
2144.1.cd \(\chi_{2144}(5, \cdot)\) None 0 40
2144.1.cg \(\chi_{2144}(41, \cdot)\) None 0 40
2144.1.ch \(\chi_{2144}(23, \cdot)\) None 0 40
2144.1.ci \(\chi_{2144}(19, \cdot)\) None 0 80
2144.1.ck \(\chi_{2144}(13, \cdot)\) None 0 80

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2144))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2144)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(268))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(536))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1072))\)\(^{\oplus 2}\)