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Properties

Label 440.1
Level 440
Weight 1
Dimension 16
Nonzero newspaces 2
Newform subspaces 7
Sturm bound 11520
Trace bound 4

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Defining parameters

Level: \( N \) = \( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 7 \)
Sturm bound: \(11520\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(440))\).

Total New Old
Modular forms 516 124 392
Cusp forms 36 16 20
Eisenstein series 480 108 372

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16 q + 2 q^{4} - 6 q^{9} + O(q^{10}) \) \( 16 q + 2 q^{4} - 6 q^{9} + 8 q^{10} - 2 q^{11} + 6 q^{14} - 4 q^{15} - 2 q^{16} - 4 q^{19} + 4 q^{20} - 2 q^{25} - 8 q^{26} - 4 q^{31} - 8 q^{34} - 4 q^{35} - 2 q^{36} - 2 q^{40} + 6 q^{41} + 2 q^{44} - 4 q^{46} + 8 q^{49} - 4 q^{55} - 12 q^{56} - 4 q^{59} - 4 q^{60} + 2 q^{64} - 4 q^{65} - 4 q^{66} + 4 q^{70} + 4 q^{71} - 4 q^{74} - 4 q^{76} - 2 q^{81} + 4 q^{86} - 8 q^{89} - 2 q^{90} + 2 q^{91} + 6 q^{94} - 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(440))\)

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
440.1.d \(\chi_{440}(21, \cdot)\) None 0 1
440.1.e \(\chi_{440}(111, \cdot)\) None 0 1
440.1.h \(\chi_{440}(419, \cdot)\) None 0 1
440.1.i \(\chi_{440}(329, \cdot)\) None 0 1
440.1.j \(\chi_{440}(241, \cdot)\) None 0 1
440.1.k \(\chi_{440}(331, \cdot)\) None 0 1
440.1.n \(\chi_{440}(199, \cdot)\) None 0 1
440.1.o \(\chi_{440}(109, \cdot)\) 440.1.o.a 1 1
440.1.o.b 1
440.1.o.c 1
440.1.o.d 1
440.1.o.e 4
440.1.q \(\chi_{440}(87, \cdot)\) None 0 2
440.1.s \(\chi_{440}(177, \cdot)\) None 0 2
440.1.u \(\chi_{440}(133, \cdot)\) None 0 2
440.1.w \(\chi_{440}(43, \cdot)\) None 0 2
440.1.ba \(\chi_{440}(29, \cdot)\) None 0 4
440.1.bb \(\chi_{440}(119, \cdot)\) None 0 4
440.1.be \(\chi_{440}(91, \cdot)\) None 0 4
440.1.bf \(\chi_{440}(41, \cdot)\) None 0 4
440.1.bg \(\chi_{440}(129, \cdot)\) None 0 4
440.1.bh \(\chi_{440}(59, \cdot)\) 440.1.bh.a 4 4
440.1.bh.b 4
440.1.bk \(\chi_{440}(31, \cdot)\) None 0 4
440.1.bl \(\chi_{440}(61, \cdot)\) None 0 4
440.1.bp \(\chi_{440}(37, \cdot)\) None 0 8
440.1.br \(\chi_{440}(83, \cdot)\) None 0 8
440.1.bt \(\chi_{440}(7, \cdot)\) None 0 8
440.1.bv \(\chi_{440}(97, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(440))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(440)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 2}\)