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Properties

Label 1197.1
Level 1197
Weight 1
Dimension 50
Nonzero newspaces 8
Newform subspaces 11
Sturm bound 103680
Trace bound 19

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Defining parameters

Level: \( N \) = \( 1197 = 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 11 \)
Sturm bound: \(103680\)
Trace bound: \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1197))\).

Total New Old
Modular forms 1904 814 1090
Cusp forms 176 50 126
Eisenstein series 1728 764 964

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 46 4 0 0

Trace form

\( 50 q + 2 q^{2} - q^{4} - q^{5} + 3 q^{7} + 4 q^{8} + O(q^{10}) \) \( 50 q + 2 q^{2} - q^{4} - q^{5} + 3 q^{7} + 4 q^{8} - q^{11} + 6 q^{13} - 3 q^{16} + 2 q^{17} + 7 q^{19} + 2 q^{20} + q^{23} - 6 q^{25} - q^{28} - 2 q^{29} + q^{35} + 4 q^{37} - 10 q^{43} - q^{44} + 4 q^{46} - q^{47} - 9 q^{49} - 6 q^{52} - 2 q^{53} + 14 q^{55} - 4 q^{58} + 5 q^{61} - 6 q^{64} - 4 q^{65} - 12 q^{67} + 2 q^{68} - 2 q^{70} - 2 q^{71} + 9 q^{73} - 2 q^{76} + 2 q^{77} - q^{80} + 2 q^{83} - 6 q^{85} + 2 q^{86} + 5 q^{91} + 2 q^{92} - 3 q^{95} - 2 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1197))\)

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
1197.1.b \(\chi_{1197}(134, \cdot)\) None 0 1
1197.1.e \(\chi_{1197}(379, \cdot)\) None 0 1
1197.1.g \(\chi_{1197}(685, \cdot)\) None 0 1
1197.1.h \(\chi_{1197}(1196, \cdot)\) 1197.1.h.a 4 1
1197.1.w \(\chi_{1197}(809, \cdot)\) None 0 2
1197.1.y \(\chi_{1197}(274, \cdot)\) None 0 2
1197.1.z \(\chi_{1197}(151, \cdot)\) None 0 2
1197.1.bc \(\chi_{1197}(331, \cdot)\) None 0 2
1197.1.bd \(\chi_{1197}(695, \cdot)\) None 0 2
1197.1.bg \(\chi_{1197}(590, \cdot)\) None 0 2
1197.1.bh \(\chi_{1197}(239, \cdot)\) None 0 2
1197.1.bj \(\chi_{1197}(46, \cdot)\) None 0 2
1197.1.bm \(\chi_{1197}(178, \cdot)\) None 0 2
1197.1.bn \(\chi_{1197}(790, \cdot)\) None 0 2
1197.1.bq \(\chi_{1197}(628, \cdot)\) None 0 2
1197.1.br \(\chi_{1197}(692, \cdot)\) None 0 2
1197.1.bs \(\chi_{1197}(962, \cdot)\) None 0 2
1197.1.bt \(\chi_{1197}(341, \cdot)\) 1197.1.bt.a 8 2
1197.1.bu \(\chi_{1197}(122, \cdot)\) None 0 2
1197.1.bv \(\chi_{1197}(920, \cdot)\) None 0 2
1197.1.bw \(\chi_{1197}(398, \cdot)\) None 0 2
1197.1.by \(\chi_{1197}(286, \cdot)\) None 0 2
1197.1.bz \(\chi_{1197}(292, \cdot)\) None 0 2
1197.1.cc \(\chi_{1197}(220, \cdot)\) None 0 2
1197.1.ce \(\chi_{1197}(514, \cdot)\) None 0 2
1197.1.cf \(\chi_{1197}(334, \cdot)\) None 0 2
1197.1.ci \(\chi_{1197}(748, \cdot)\) 1197.1.ci.a 2 2
1197.1.ci.b 2
1197.1.ci.c 4
1197.1.cj \(\chi_{1197}(626, \cdot)\) None 0 2
1197.1.ck \(\chi_{1197}(734, \cdot)\) None 0 2
1197.1.cl \(\chi_{1197}(164, \cdot)\) None 0 2
1197.1.cm \(\chi_{1197}(191, \cdot)\) None 0 2
1197.1.cp \(\chi_{1197}(995, \cdot)\) None 0 2
1197.1.cq \(\chi_{1197}(767, \cdot)\) None 0 2
1197.1.ct \(\chi_{1197}(373, \cdot)\) None 0 2
1197.1.cu \(\chi_{1197}(778, \cdot)\) None 0 2
1197.1.cx \(\chi_{1197}(445, \cdot)\) None 0 2
1197.1.cz \(\chi_{1197}(37, \cdot)\) 1197.1.cz.a 2 2
1197.1.cz.b 4
1197.1.da \(\chi_{1197}(487, \cdot)\) None 0 2
1197.1.dd \(\chi_{1197}(316, \cdot)\) None 0 2
1197.1.de \(\chi_{1197}(197, \cdot)\) None 0 2
1197.1.dh \(\chi_{1197}(296, \cdot)\) None 0 2
1197.1.di \(\chi_{1197}(305, \cdot)\) None 0 2
1197.1.dk \(\chi_{1197}(254, \cdot)\) None 0 2
1197.1.dn \(\chi_{1197}(533, \cdot)\) None 0 2
1197.1.do \(\chi_{1197}(11, \cdot)\) None 0 2
1197.1.dr \(\chi_{1197}(88, \cdot)\) None 0 2
1197.1.ds \(\chi_{1197}(673, \cdot)\) None 0 2
1197.1.dv \(\chi_{1197}(835, \cdot)\) None 0 2
1197.1.dw \(\chi_{1197}(1018, \cdot)\) None 0 2
1197.1.dy \(\chi_{1197}(236, \cdot)\) None 0 2
1197.1.dz \(\chi_{1197}(227, \cdot)\) None 0 2
1197.1.ea \(\chi_{1197}(293, \cdot)\) None 0 2
1197.1.ec \(\chi_{1197}(349, \cdot)\) None 0 2
1197.1.ed \(\chi_{1197}(115, \cdot)\) None 0 2
1197.1.eg \(\chi_{1197}(976, \cdot)\) None 0 2
1197.1.eh \(\chi_{1197}(278, \cdot)\) None 0 2
1197.1.es \(\chi_{1197}(257, \cdot)\) None 0 6
1197.1.et \(\chi_{1197}(41, \cdot)\) None 0 6
1197.1.ew \(\chi_{1197}(143, \cdot)\) None 0 6
1197.1.ex \(\chi_{1197}(73, \cdot)\) 1197.1.ex.a 6 6
1197.1.ey \(\chi_{1197}(55, \cdot)\) None 0 6
1197.1.ez \(\chi_{1197}(187, \cdot)\) None 0 6
1197.1.fa \(\chi_{1197}(367, \cdot)\) None 0 6
1197.1.fb \(\chi_{1197}(61, \cdot)\) None 0 6
1197.1.fc \(\chi_{1197}(139, \cdot)\) None 0 6
1197.1.ff \(\chi_{1197}(167, \cdot)\) None 0 6
1197.1.fg \(\chi_{1197}(59, \cdot)\) None 0 6
1197.1.fh \(\chi_{1197}(383, \cdot)\) None 0 6
1197.1.fi \(\chi_{1197}(173, \cdot)\) None 0 6
1197.1.fn \(\chi_{1197}(314, \cdot)\) None 0 6
1197.1.fo \(\chi_{1197}(89, \cdot)\) None 0 6
1197.1.fp \(\chi_{1197}(199, \cdot)\) 1197.1.fp.a 6 6
1197.1.fq \(\chi_{1197}(328, \cdot)\) None 0 6
1197.1.fr \(\chi_{1197}(481, \cdot)\) None 0 6
1197.1.fs \(\chi_{1197}(233, \cdot)\) None 0 6
1197.1.fv \(\chi_{1197}(23, \cdot)\) None 0 6
1197.1.fw \(\chi_{1197}(176, \cdot)\) None 0 6
1197.1.ga \(\chi_{1197}(148, \cdot)\) None 0 6
1197.1.gb \(\chi_{1197}(193, \cdot)\) None 0 6
1197.1.gc \(\chi_{1197}(67, \cdot)\) None 0 6
1197.1.gd \(\chi_{1197}(466, \cdot)\) None 0 6
1197.1.gi \(\chi_{1197}(109, \cdot)\) 1197.1.gi.a 6 6
1197.1.gj \(\chi_{1197}(127, \cdot)\) None 0 6
1197.1.gk \(\chi_{1197}(386, \cdot)\) None 0 6
1197.1.gl \(\chi_{1197}(44, \cdot)\) None 0 6
1197.1.gq \(\chi_{1197}(137, \cdot)\) None 0 6
1197.1.gr \(\chi_{1197}(158, \cdot)\) None 0 6
1197.1.gs \(\chi_{1197}(347, \cdot)\) None 0 6
1197.1.gt \(\chi_{1197}(92, \cdot)\) None 0 6
1197.1.gx \(\chi_{1197}(22, \cdot)\) None 0 6
1197.1.gy \(\chi_{1197}(184, \cdot)\) None 0 6
1197.1.hb \(\chi_{1197}(298, \cdot)\) 1197.1.hb.a 6 6

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1197))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1197)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(399))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1197))\)\(^{\oplus 1}\)