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Properties

Label 2200.1
Level 2200
Weight 1
Dimension 148
Nonzero newspaces 6
Newform subspaces 21
Sturm bound 288000
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2200 = 2^{3} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 21 \)
Sturm bound: \(288000\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2200))\).

Total New Old
Modular forms 3692 886 2806
Cusp forms 332 148 184
Eisenstein series 3360 738 2622

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 148 0 0 0

Trace form

\( 148 q + q^{2} + 2 q^{3} - q^{4} - 3 q^{6} + q^{8} + 9 q^{9} + O(q^{10}) \) \( 148 q + q^{2} + 2 q^{3} - q^{4} - 3 q^{6} + q^{8} + 9 q^{9} - q^{11} + 2 q^{12} - 6 q^{14} - 5 q^{16} + 2 q^{17} - 2 q^{18} + q^{19} + q^{22} - 3 q^{24} - 16 q^{26} - q^{27} - 12 q^{31} - 4 q^{32} - 3 q^{33} + 10 q^{34} - 8 q^{36} + 2 q^{38} - 12 q^{41} + 2 q^{43} - 6 q^{44} - 4 q^{46} + 2 q^{48} - 7 q^{49} - 25 q^{51} + 4 q^{54} - 12 q^{56} - q^{57} + q^{59} - q^{64} - 14 q^{66} + 2 q^{67} + 2 q^{68} - 4 q^{71} + 3 q^{72} + 2 q^{73} + 4 q^{74} - 2 q^{76} - 6 q^{81} - 3 q^{82} - 3 q^{83} - 31 q^{86} + q^{88} + 10 q^{89} + 22 q^{91} - 6 q^{94} + 2 q^{96} - 3 q^{97} - 4 q^{98} + 5 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2200))\)

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
2200.1.d \(\chi_{2200}(901, \cdot)\) 2200.1.d.a 1 1
2200.1.d.b 1
2200.1.d.c 1
2200.1.d.d 1
2200.1.d.e 2
2200.1.d.f 2
2200.1.d.g 4
2200.1.e \(\chi_{2200}(551, \cdot)\) None 0 1
2200.1.h \(\chi_{2200}(1299, \cdot)\) None 0 1
2200.1.i \(\chi_{2200}(1649, \cdot)\) None 0 1
2200.1.j \(\chi_{2200}(2001, \cdot)\) None 0 1
2200.1.k \(\chi_{2200}(1651, \cdot)\) None 0 1
2200.1.n \(\chi_{2200}(199, \cdot)\) None 0 1
2200.1.o \(\chi_{2200}(549, \cdot)\) 2200.1.o.a 2 1
2200.1.o.b 2
2200.1.q \(\chi_{2200}(1143, \cdot)\) None 0 2
2200.1.s \(\chi_{2200}(793, \cdot)\) None 0 2
2200.1.u \(\chi_{2200}(1893, \cdot)\) None 0 2
2200.1.w \(\chi_{2200}(43, \cdot)\) 2200.1.w.a 4 2
2200.1.w.b 4
2200.1.w.c 8
2200.1.bg \(\chi_{2200}(369, \cdot)\) None 0 4
2200.1.bh \(\chi_{2200}(59, \cdot)\) None 0 4
2200.1.bk \(\chi_{2200}(191, \cdot)\) None 0 4
2200.1.bl \(\chi_{2200}(261, \cdot)\) None 0 4
2200.1.bo \(\chi_{2200}(331, \cdot)\) None 0 4
2200.1.bp \(\chi_{2200}(241, \cdot)\) None 0 4
2200.1.bu \(\chi_{2200}(559, \cdot)\) None 0 4
2200.1.bv \(\chi_{2200}(29, \cdot)\) None 0 4
2200.1.bw \(\chi_{2200}(149, \cdot)\) None 0 4
2200.1.bx \(\chi_{2200}(1029, \cdot)\) None 0 4
2200.1.by \(\chi_{2200}(119, \cdot)\) None 0 4
2200.1.bz \(\chi_{2200}(159, \cdot)\) None 0 4
2200.1.ca \(\chi_{2200}(399, \cdot)\) None 0 4
2200.1.cb \(\chi_{2200}(469, \cdot)\) None 0 4
2200.1.ck \(\chi_{2200}(921, \cdot)\) None 0 4
2200.1.cl \(\chi_{2200}(251, \cdot)\) 2200.1.cl.a 4 4
2200.1.cl.b 8
2200.1.cl.c 8
2200.1.cl.d 8
2200.1.cm \(\chi_{2200}(291, \cdot)\) None 0 4
2200.1.cn \(\chi_{2200}(91, \cdot)\) None 0 4
2200.1.co \(\chi_{2200}(41, \cdot)\) None 0 4
2200.1.cp \(\chi_{2200}(601, \cdot)\) None 0 4
2200.1.cq \(\chi_{2200}(481, \cdot)\) None 0 4
2200.1.cr \(\chi_{2200}(691, \cdot)\) None 0 4
2200.1.ct \(\chi_{2200}(109, \cdot)\) None 0 4
2200.1.cu \(\chi_{2200}(639, \cdot)\) None 0 4
2200.1.cv \(\chi_{2200}(111, \cdot)\) None 0 4
2200.1.cw \(\chi_{2200}(21, \cdot)\) None 0 4
2200.1.cz \(\chi_{2200}(179, \cdot)\) None 0 4
2200.1.da \(\chi_{2200}(689, \cdot)\) None 0 4
2200.1.db \(\chi_{2200}(249, \cdot)\) None 0 4
2200.1.dc \(\chi_{2200}(569, \cdot)\) None 0 4
2200.1.dd \(\chi_{2200}(499, \cdot)\) 2200.1.dd.a 8 4
2200.1.dd.b 16
2200.1.de \(\chi_{2200}(339, \cdot)\) None 0 4
2200.1.df \(\chi_{2200}(379, \cdot)\) None 0 4
2200.1.dg \(\chi_{2200}(129, \cdot)\) None 0 4
2200.1.dp \(\chi_{2200}(61, \cdot)\) None 0 4
2200.1.dq \(\chi_{2200}(31, \cdot)\) None 0 4
2200.1.dr \(\chi_{2200}(911, \cdot)\) None 0 4
2200.1.ds \(\chi_{2200}(751, \cdot)\) None 0 4
2200.1.dt \(\chi_{2200}(821, \cdot)\) None 0 4
2200.1.du \(\chi_{2200}(101, \cdot)\) None 0 4
2200.1.dv \(\chi_{2200}(981, \cdot)\) None 0 4
2200.1.dw \(\chi_{2200}(511, \cdot)\) None 0 4
2200.1.ef \(\chi_{2200}(329, \cdot)\) None 0 4
2200.1.eg \(\chi_{2200}(419, \cdot)\) None 0 4
2200.1.ej \(\chi_{2200}(629, \cdot)\) None 0 4
2200.1.ek \(\chi_{2200}(839, \cdot)\) None 0 4
2200.1.em \(\chi_{2200}(731, \cdot)\) None 0 4
2200.1.en \(\chi_{2200}(281, \cdot)\) None 0 4
2200.1.eq \(\chi_{2200}(83, \cdot)\) None 0 8
2200.1.es \(\chi_{2200}(37, \cdot)\) None 0 8
2200.1.eu \(\chi_{2200}(97, \cdot)\) None 0 8
2200.1.ew \(\chi_{2200}(327, \cdot)\) None 0 8
2200.1.ez \(\chi_{2200}(113, \cdot)\) None 0 8
2200.1.fb \(\chi_{2200}(63, \cdot)\) None 0 8
2200.1.fd \(\chi_{2200}(93, \cdot)\) None 0 8
2200.1.ff \(\chi_{2200}(123, \cdot)\) None 0 8
2200.1.fi \(\chi_{2200}(483, \cdot)\) None 0 8
2200.1.fj \(\chi_{2200}(387, \cdot)\) None 0 8
2200.1.fm \(\chi_{2200}(133, \cdot)\) None 0 8
2200.1.fn \(\chi_{2200}(597, \cdot)\) None 0 8
2200.1.fp \(\chi_{2200}(333, \cdot)\) None 0 8
2200.1.fr \(\chi_{2200}(107, \cdot)\) 2200.1.fr.a 16 8
2200.1.fr.b 16
2200.1.fr.c 32
2200.1.ft \(\chi_{2200}(7, \cdot)\) None 0 8
2200.1.fw \(\chi_{2200}(177, \cdot)\) None 0 8
2200.1.fx \(\chi_{2200}(433, \cdot)\) None 0 8
2200.1.fz \(\chi_{2200}(137, \cdot)\) None 0 8
2200.1.gb \(\chi_{2200}(447, \cdot)\) None 0 8
2200.1.ge \(\chi_{2200}(87, \cdot)\) None 0 8
2200.1.gf \(\chi_{2200}(127, \cdot)\) None 0 8
2200.1.gh \(\chi_{2200}(257, \cdot)\) None 0 8
2200.1.gj \(\chi_{2200}(227, \cdot)\) None 0 8
2200.1.gl \(\chi_{2200}(317, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2200))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2200)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1100))\)\(^{\oplus 2}\)