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Properties

Label 884.1
Level 884
Weight 1
Dimension 122
Nonzero newspaces 11
Newform subspaces 25
Sturm bound 48384
Trace bound 20

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Defining parameters

Level: \( N \) = \( 884 = 2^{2} \cdot 13 \cdot 17 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 11 \)
Newform subspaces: \( 25 \)
Sturm bound: \(48384\)
Trace bound: \(20\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(884))\).

Total New Old
Modular forms 1092 454 638
Cusp forms 132 122 10
Eisenstein series 960 332 628

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 122 0 0 0

Trace form

\( 122 q + 2 q^{2} + 4 q^{5} - 4 q^{8} + O(q^{10}) \) \( 122 q + 2 q^{2} + 4 q^{5} - 4 q^{8} - 10 q^{10} - 4 q^{13} + 12 q^{14} - 8 q^{16} - 11 q^{17} - 12 q^{18} - 10 q^{20} + 16 q^{21} + 12 q^{22} - 10 q^{25} - 6 q^{26} - 14 q^{29} - 8 q^{30} + 2 q^{32} + 16 q^{33} + 2 q^{34} - 2 q^{37} - 4 q^{38} + 4 q^{40} - 10 q^{41} - 8 q^{42} - 10 q^{45} - 4 q^{49} - 10 q^{52} - 16 q^{53} - 4 q^{56} - 2 q^{58} + 10 q^{61} - 4 q^{62} - 6 q^{64} - 6 q^{65} - 8 q^{66} - 19 q^{68} - 16 q^{69} - 14 q^{72} - 4 q^{73} - 10 q^{74} - 2 q^{80} - 16 q^{81} - 10 q^{82} - 8 q^{84} - 7 q^{85} - 4 q^{88} + 4 q^{89} - 4 q^{90} + 16 q^{93} - 4 q^{94} + 4 q^{97} + 10 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(884))\)

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
884.1.c \(\chi_{884}(103, \cdot)\) None 0 1
884.1.d \(\chi_{884}(443, \cdot)\) None 0 1
884.1.g \(\chi_{884}(339, \cdot)\) None 0 1
884.1.h \(\chi_{884}(883, \cdot)\) 884.1.h.a 1 1
884.1.h.b 1
884.1.h.c 2
884.1.h.d 2
884.1.h.e 4
884.1.j \(\chi_{884}(577, \cdot)\) None 0 2
884.1.l \(\chi_{884}(489, \cdot)\) None 0 2
884.1.n \(\chi_{884}(259, \cdot)\) 884.1.n.a 2 2
884.1.n.b 2
884.1.q \(\chi_{884}(183, \cdot)\) None 0 2
884.1.s \(\chi_{884}(21, \cdot)\) None 0 2
884.1.u \(\chi_{884}(681, \cdot)\) None 0 2
884.1.v \(\chi_{884}(679, \cdot)\) 884.1.v.a 2 2
884.1.v.b 2
884.1.v.c 2
884.1.v.d 2
884.1.v.e 4
884.1.x \(\chi_{884}(407, \cdot)\) 884.1.x.a 8 2
884.1.y \(\chi_{884}(511, \cdot)\) None 0 2
884.1.bb \(\chi_{884}(35, \cdot)\) None 0 2
884.1.bd \(\chi_{884}(161, \cdot)\) None 0 4
884.1.be \(\chi_{884}(287, \cdot)\) None 0 4
884.1.bg \(\chi_{884}(155, \cdot)\) 884.1.bg.a 4 4
884.1.bg.b 4
884.1.bg.c 4
884.1.bg.d 4
884.1.bj \(\chi_{884}(229, \cdot)\) None 0 4
884.1.bk \(\chi_{884}(137, \cdot)\) None 0 4
884.1.bn \(\chi_{884}(557, \cdot)\) None 0 4
884.1.bp \(\chi_{884}(55, \cdot)\) 884.1.bp.a 4 4
884.1.bp.b 4
884.1.bq \(\chi_{884}(251, \cdot)\) None 0 4
884.1.bs \(\chi_{884}(89, \cdot)\) None 0 4
884.1.bv \(\chi_{884}(33, \cdot)\) None 0 4
884.1.bw \(\chi_{884}(99, \cdot)\) 884.1.bw.a 8 8
884.1.bz \(\chi_{884}(105, \cdot)\) None 0 8
884.1.cb \(\chi_{884}(129, \cdot)\) None 0 8
884.1.cc \(\chi_{884}(31, \cdot)\) 884.1.cc.a 8 8
884.1.ce \(\chi_{884}(253, \cdot)\) None 0 8
884.1.ch \(\chi_{884}(87, \cdot)\) None 0 8
884.1.cj \(\chi_{884}(43, \cdot)\) 884.1.cj.a 8 8
884.1.cj.b 8
884.1.ck \(\chi_{884}(93, \cdot)\) None 0 8
884.1.cn \(\chi_{884}(63, \cdot)\) 884.1.cn.a 16 16
884.1.co \(\chi_{884}(173, \cdot)\) None 0 16
884.1.cq \(\chi_{884}(29, \cdot)\) None 0 16
884.1.ct \(\chi_{884}(7, \cdot)\) 884.1.ct.a 16 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(884))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(884)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)