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Properties

Label 2964.1
Level 2964
Weight 1
Dimension 148
Nonzero newspaces 17
Newform subspaces 34
Sturm bound 483840
Trace bound 19

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Defining parameters

Level: \( N \) = \( 2964 = 2^{2} \cdot 3 \cdot 13 \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 17 \)
Newform subspaces: \( 34 \)
Sturm bound: \(483840\)
Trace bound: \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2964))\).

Total New Old
Modular forms 4762 892 3870
Cusp forms 442 148 294
Eisenstein series 4320 744 3576

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 132 0 16 0

Trace form

\( 148 q + 4 q^{7} + 12 q^{9} + O(q^{10}) \) \( 148 q + 4 q^{7} + 12 q^{9} + 3 q^{13} + 8 q^{19} + 10 q^{21} + 6 q^{27} - 8 q^{30} + 4 q^{31} + 8 q^{36} + 4 q^{37} - 8 q^{39} - 8 q^{42} + 2 q^{43} + 8 q^{45} + 10 q^{49} + 4 q^{57} + 8 q^{58} - 28 q^{61} - 20 q^{63} + 24 q^{64} - 2 q^{67} + 26 q^{73} - 8 q^{75} - 12 q^{79} + 20 q^{81} - 8 q^{82} + 8 q^{85} - 2 q^{91} - 8 q^{93} + 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2964))\)

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
2964.1.b \(\chi_{2964}(493, \cdot)\) None 0 1
2964.1.e \(\chi_{2964}(911, \cdot)\) None 0 1
2964.1.f \(\chi_{2964}(989, \cdot)\) None 0 1
2964.1.i \(\chi_{2964}(571, \cdot)\) None 0 1
2964.1.k \(\chi_{2964}(1483, \cdot)\) None 0 1
2964.1.l \(\chi_{2964}(77, \cdot)\) None 0 1
2964.1.o \(\chi_{2964}(2963, \cdot)\) 2964.1.o.a 1 1
2964.1.o.b 1
2964.1.o.c 1
2964.1.o.d 1
2964.1.o.e 1
2964.1.o.f 1
2964.1.o.g 1
2964.1.o.h 1
2964.1.p \(\chi_{2964}(1405, \cdot)\) None 0 1
2964.1.v \(\chi_{2964}(229, \cdot)\) None 0 2
2964.1.w \(\chi_{2964}(151, \cdot)\) None 0 2
2964.1.y \(\chi_{2964}(1331, \cdot)\) None 0 2
2964.1.bb \(\chi_{2964}(1253, \cdot)\) None 0 2
2964.1.bc \(\chi_{2964}(2623, \cdot)\) None 0 2
2964.1.bf \(\chi_{2964}(1673, \cdot)\) None 0 2
2964.1.bg \(\chi_{2964}(1595, \cdot)\) 2964.1.bg.a 8 2
2964.1.bg.b 8
2964.1.bj \(\chi_{2964}(2545, \cdot)\) None 0 2
2964.1.bk \(\chi_{2964}(235, \cdot)\) None 0 2
2964.1.bn \(\chi_{2964}(1793, \cdot)\) None 0 2
2964.1.bo \(\chi_{2964}(373, \cdot)\) None 0 2
2964.1.bp \(\chi_{2964}(217, \cdot)\) None 0 2
2964.1.br \(\chi_{2964}(335, \cdot)\) None 0 2
2964.1.bs \(\chi_{2964}(179, \cdot)\) None 0 2
2964.1.bu \(\chi_{2964}(881, \cdot)\) 2964.1.bu.a 2 2
2964.1.bu.b 2
2964.1.bx \(\chi_{2964}(1037, \cdot)\) 2964.1.bx.a 2 2
2964.1.bx.b 2
2964.1.by \(\chi_{2964}(919, \cdot)\) None 0 2
2964.1.cb \(\chi_{2964}(1075, \cdot)\) None 0 2
2964.1.cc \(\chi_{2964}(1091, \cdot)\) None 0 2
2964.1.ce \(\chi_{2964}(2497, \cdot)\) None 0 2
2964.1.cg \(\chi_{2964}(1585, \cdot)\) None 0 2
2964.1.ch \(\chi_{2964}(2003, \cdot)\) None 0 2
2964.1.cj \(\chi_{2964}(1531, \cdot)\) None 0 2
2964.1.cm \(\chi_{2964}(1375, \cdot)\) None 0 2
2964.1.cn \(\chi_{2964}(581, \cdot)\) 2964.1.cn.a 2 2
2964.1.cn.b 2
2964.1.cq \(\chi_{2964}(425, \cdot)\) 2964.1.cq.a 2 2
2964.1.cq.b 2
2964.1.cs \(\chi_{2964}(107, \cdot)\) None 0 2
2964.1.ct \(\chi_{2964}(2843, \cdot)\) None 0 2
2964.1.cw \(\chi_{2964}(673, \cdot)\) None 0 2
2964.1.cx \(\chi_{2964}(829, \cdot)\) None 0 2
2964.1.da \(\chi_{2964}(2705, \cdot)\) None 0 2
2964.1.db \(\chi_{2964}(2287, \cdot)\) None 0 2
2964.1.dd \(\chi_{2964}(2089, \cdot)\) None 0 2
2964.1.de \(\chi_{2964}(2051, \cdot)\) None 0 2
2964.1.dh \(\chi_{2964}(2129, \cdot)\) None 0 2
2964.1.di \(\chi_{2964}(2167, \cdot)\) None 0 2
2964.1.do \(\chi_{2964}(349, \cdot)\) None 0 4
2964.1.dp \(\chi_{2964}(331, \cdot)\) None 0 4
2964.1.dr \(\chi_{2964}(1025, \cdot)\) 2964.1.dr.a 4 4
2964.1.dr.b 4
2964.1.dt \(\chi_{2964}(749, \cdot)\) None 0 4
2964.1.du \(\chi_{2964}(449, \cdot)\) 2964.1.du.a 4 4
2964.1.du.b 4
2964.1.dy \(\chi_{2964}(1103, \cdot)\) None 0 4
2964.1.eb \(\chi_{2964}(83, \cdot)\) None 0 4
2964.1.ec \(\chi_{2964}(11, \cdot)\) None 0 4
2964.1.ee \(\chi_{2964}(379, \cdot)\) None 0 4
2964.1.eh \(\chi_{2964}(31, \cdot)\) None 0 4
2964.1.ei \(\chi_{2964}(487, \cdot)\) None 0 4
2964.1.ej \(\chi_{2964}(457, \cdot)\) None 0 4
2964.1.el \(\chi_{2964}(577, \cdot)\) None 0 4
2964.1.em \(\chi_{2964}(505, \cdot)\) None 0 4
2964.1.ep \(\chi_{2964}(695, \cdot)\) None 0 4
2964.1.es \(\chi_{2964}(293, \cdot)\) 2964.1.es.a 4 4
2964.1.es.b 4
2964.1.et \(\chi_{2964}(433, \cdot)\) None 0 6
2964.1.ev \(\chi_{2964}(55, \cdot)\) None 0 6
2964.1.ey \(\chi_{2964}(659, \cdot)\) None 0 6
2964.1.fa \(\chi_{2964}(329, \cdot)\) 2964.1.fa.a 6 6
2964.1.fb \(\chi_{2964}(415, \cdot)\) None 0 6
2964.1.fc \(\chi_{2964}(43, \cdot)\) None 0 6
2964.1.fd \(\chi_{2964}(469, \cdot)\) None 0 6
2964.1.ff \(\chi_{2964}(1381, \cdot)\) None 0 6
2964.1.fi \(\chi_{2964}(1277, \cdot)\) 2964.1.fi.a 6 6
2964.1.fk \(\chi_{2964}(365, \cdot)\) None 0 6
2964.1.fm \(\chi_{2964}(1115, \cdot)\) None 0 6
2964.1.fo \(\chi_{2964}(155, \cdot)\) None 0 6
2964.1.fp \(\chi_{2964}(287, \cdot)\) None 0 6
2964.1.fr \(\chi_{2964}(887, \cdot)\) None 0 6
2964.1.ft \(\chi_{2964}(233, \cdot)\) 2964.1.ft.a 6 6
2964.1.ft.b 6
2964.1.fv \(\chi_{2964}(17, \cdot)\) 2964.1.fv.a 6 6
2964.1.fy \(\chi_{2964}(205, \cdot)\) None 0 6
2964.1.ga \(\chi_{2964}(181, \cdot)\) None 0 6
2964.1.gc \(\chi_{2964}(367, \cdot)\) None 0 6
2964.1.ge \(\chi_{2964}(859, \cdot)\) None 0 6
2964.1.gf \(\chi_{2964}(1049, \cdot)\) 2964.1.gf.a 6 6
2964.1.gh \(\chi_{2964}(1343, \cdot)\) None 0 6
2964.1.gj \(\chi_{2964}(199, \cdot)\) None 0 6
2964.1.gl \(\chi_{2964}(1153, \cdot)\) None 0 6
2964.1.go \(\chi_{2964}(85, \cdot)\) None 0 12
2964.1.gp \(\chi_{2964}(223, \cdot)\) None 0 12
2964.1.gq \(\chi_{2964}(41, \cdot)\) 2964.1.gq.a 12 12
2964.1.gr \(\chi_{2964}(119, \cdot)\) None 0 12
2964.1.gy \(\chi_{2964}(307, \cdot)\) None 0 12
2964.1.gz \(\chi_{2964}(73, \cdot)\) None 0 12
2964.1.ha \(\chi_{2964}(397, \cdot)\) None 0 12
2964.1.hb \(\chi_{2964}(67, \cdot)\) None 0 12
2964.1.hc \(\chi_{2964}(47, \cdot)\) None 0 12
2964.1.hd \(\chi_{2964}(281, \cdot)\) 2964.1.hd.a 12 12
2964.1.hd.b 12
2964.1.he \(\chi_{2964}(89, \cdot)\) 2964.1.he.a 12 12
2964.1.hf \(\chi_{2964}(275, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2964))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2964)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(247))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(494))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(741))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(988))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1482))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2964))\)\(^{\oplus 1}\)