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Properties

Label 880.1
Level 880
Weight 1
Dimension 23
Nonzero newspaces 3
Newform subspaces 7
Sturm bound 46080
Trace bound 1

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Defining parameters

Level: \( N \) = \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 7 \)
Sturm bound: \(46080\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(880))\).

Total New Old
Modular forms 1212 265 947
Cusp forms 92 23 69
Eisenstein series 1120 242 878

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 23 0 0 0

Trace form

\( 23 q - 3 q^{9} + O(q^{10}) \) \( 23 q - 3 q^{9} + 3 q^{11} + 8 q^{14} - 3 q^{15} + 8 q^{20} - 8 q^{44} - 3 q^{45} - 11 q^{49} - 12 q^{53} + 8 q^{59} + 6 q^{69} - 8 q^{70} - 3 q^{75} - 17 q^{81} - 8 q^{86} - 8 q^{91} + 12 q^{93} - 3 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(880))\)

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
880.1.d \(\chi_{880}(681, \cdot)\) None 0 1
880.1.e \(\chi_{880}(111, \cdot)\) None 0 1
880.1.h \(\chi_{880}(199, \cdot)\) None 0 1
880.1.i \(\chi_{880}(769, \cdot)\) 880.1.i.a 1 1
880.1.i.b 2
880.1.j \(\chi_{880}(241, \cdot)\) None 0 1
880.1.k \(\chi_{880}(551, \cdot)\) None 0 1
880.1.n \(\chi_{880}(639, \cdot)\) None 0 1
880.1.o \(\chi_{880}(329, \cdot)\) None 0 1
880.1.q \(\chi_{880}(43, \cdot)\) None 0 2
880.1.r \(\chi_{880}(573, \cdot)\) None 0 2
880.1.u \(\chi_{880}(419, \cdot)\) None 0 2
880.1.x \(\chi_{880}(109, \cdot)\) 880.1.x.a 8 2
880.1.y \(\chi_{880}(527, \cdot)\) 880.1.y.a 2 2
880.1.y.b 2
880.1.y.c 4
880.1.y.d 4
880.1.ba \(\chi_{880}(177, \cdot)\) None 0 2
880.1.bc \(\chi_{880}(617, \cdot)\) None 0 2
880.1.be \(\chi_{880}(87, \cdot)\) None 0 2
880.1.bg \(\chi_{880}(21, \cdot)\) None 0 2
880.1.bj \(\chi_{880}(331, \cdot)\) None 0 2
880.1.bm \(\chi_{880}(483, \cdot)\) None 0 2
880.1.bn \(\chi_{880}(133, \cdot)\) None 0 2
880.1.bq \(\chi_{880}(249, \cdot)\) None 0 4
880.1.br \(\chi_{880}(159, \cdot)\) None 0 4
880.1.bu \(\chi_{880}(71, \cdot)\) None 0 4
880.1.bv \(\chi_{880}(161, \cdot)\) None 0 4
880.1.bw \(\chi_{880}(129, \cdot)\) None 0 4
880.1.bx \(\chi_{880}(119, \cdot)\) None 0 4
880.1.ca \(\chi_{880}(31, \cdot)\) None 0 4
880.1.cb \(\chi_{880}(41, \cdot)\) None 0 4
880.1.ce \(\chi_{880}(53, \cdot)\) None 0 8
880.1.cf \(\chi_{880}(83, \cdot)\) None 0 8
880.1.cj \(\chi_{880}(91, \cdot)\) None 0 8
880.1.ck \(\chi_{880}(61, \cdot)\) None 0 8
880.1.cn \(\chi_{880}(137, \cdot)\) None 0 8
880.1.cp \(\chi_{880}(7, \cdot)\) None 0 8
880.1.cr \(\chi_{880}(63, \cdot)\) None 0 8
880.1.ct \(\chi_{880}(97, \cdot)\) None 0 8
880.1.cv \(\chi_{880}(29, \cdot)\) None 0 8
880.1.cw \(\chi_{880}(59, \cdot)\) None 0 8
880.1.da \(\chi_{880}(37, \cdot)\) None 0 8
880.1.db \(\chi_{880}(123, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(880))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(880)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 2}\)