Properties

Label 2015.1
Level 2015
Weight 1
Dimension 52
Nonzero newspaces 3
Newform subspaces 11
Sturm bound 322560
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 11 \)
Sturm bound: \(322560\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2015))\).

Total New Old
Modular forms 2950 1968 982
Cusp forms 70 52 18
Eisenstein series 2880 1916 964

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 44 8 0 0

Trace form

\( 52q + 16q^{4} + 16q^{9} + O(q^{10}) \) \( 52q + 16q^{4} + 16q^{9} - 8q^{10} - 16q^{14} + 16q^{16} + 4q^{19} + 12q^{25} - 8q^{31} - 8q^{35} + 4q^{36} + 20q^{39} + 20q^{41} - 8q^{45} + 16q^{49} - 24q^{51} - 12q^{56} - 4q^{59} - 8q^{66} - 20q^{69} + 4q^{71} + 8q^{81} - 12q^{90} - 8q^{94} - 8q^{95} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2015))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2015.1.b \(\chi_{2015}(1611, \cdot)\) None 0 1
2015.1.e \(\chi_{2015}(1704, \cdot)\) None 0 1
2015.1.g \(\chi_{2015}(1301, \cdot)\) None 0 1
2015.1.h \(\chi_{2015}(2014, \cdot)\) 2015.1.h.a 4 1
2015.1.h.b 6
2015.1.h.c 6
2015.1.h.d 6
2015.1.h.e 6
2015.1.n \(\chi_{2015}(278, \cdot)\) None 0 2
2015.1.p \(\chi_{2015}(1334, \cdot)\) None 0 2
2015.1.r \(\chi_{2015}(1117, \cdot)\) None 0 2
2015.1.s \(\chi_{2015}(807, \cdot)\) None 0 2
2015.1.v \(\chi_{2015}(931, \cdot)\) None 0 2
2015.1.x \(\chi_{2015}(1487, \cdot)\) None 0 2
2015.1.z \(\chi_{2015}(274, \cdot)\) None 0 2
2015.1.bc \(\chi_{2015}(181, \cdot)\) None 0 2
2015.1.bd \(\chi_{2015}(1556, \cdot)\) None 0 2
2015.1.bf \(\chi_{2015}(309, \cdot)\) 2015.1.bf.a 8 2
2015.1.bg \(\chi_{2015}(1804, \cdot)\) None 0 2
2015.1.bi \(\chi_{2015}(471, \cdot)\) None 0 2
2015.1.bj \(\chi_{2015}(61, \cdot)\) None 0 2
2015.1.bl \(\chi_{2015}(719, \cdot)\) None 0 2
2015.1.bn \(\chi_{2015}(316, \cdot)\) None 0 2
2015.1.bp \(\chi_{2015}(874, \cdot)\) None 0 2
2015.1.bq \(\chi_{2015}(464, \cdot)\) 2015.1.bq.a 2 2
2015.1.bq.b 2
2015.1.bq.c 4
2015.1.bq.d 4
2015.1.bq.e 4
2015.1.bt \(\chi_{2015}(836, \cdot)\) None 0 2
2015.1.bu \(\chi_{2015}(1401, \cdot)\) None 0 2
2015.1.bw \(\chi_{2015}(1959, \cdot)\) None 0 2
2015.1.by \(\chi_{2015}(584, \cdot)\) None 0 2
2015.1.bz \(\chi_{2015}(781, \cdot)\) None 0 2
2015.1.cb \(\chi_{2015}(519, \cdot)\) None 0 4
2015.1.cc \(\chi_{2015}(976, \cdot)\) None 0 4
2015.1.ce \(\chi_{2015}(209, \cdot)\) None 0 4
2015.1.ch \(\chi_{2015}(116, \cdot)\) None 0 4
2015.1.cj \(\chi_{2015}(502, \cdot)\) None 0 4
2015.1.ck \(\chi_{2015}(553, \cdot)\) None 0 4
2015.1.cm \(\chi_{2015}(522, \cdot)\) None 0 4
2015.1.co \(\chi_{2015}(1332, \cdot)\) None 0 4
2015.1.cq \(\chi_{2015}(149, \cdot)\) None 0 4
2015.1.ct \(\chi_{2015}(346, \cdot)\) None 0 4
2015.1.cu \(\chi_{2015}(466, \cdot)\) None 0 4
2015.1.cw \(\chi_{2015}(366, \cdot)\) None 0 4
2015.1.cz \(\chi_{2015}(118, \cdot)\) None 0 4
2015.1.da \(\chi_{2015}(428, \cdot)\) None 0 4
2015.1.dd \(\chi_{2015}(563, \cdot)\) None 0 4
2015.1.df \(\chi_{2015}(87, \cdot)\) None 0 4
2015.1.dh \(\chi_{2015}(373, \cdot)\) None 0 4
2015.1.di \(\chi_{2015}(842, \cdot)\) None 0 4
2015.1.dk \(\chi_{2015}(218, \cdot)\) None 0 4
2015.1.dm \(\chi_{2015}(997, \cdot)\) None 0 4
2015.1.dp \(\chi_{2015}(304, \cdot)\) None 0 4
2015.1.dq \(\chi_{2015}(769, \cdot)\) None 0 4
2015.1.ds \(\chi_{2015}(249, \cdot)\) None 0 4
2015.1.du \(\chi_{2015}(1276, \cdot)\) None 0 4
2015.1.dw \(\chi_{2015}(657, \cdot)\) None 0 4
2015.1.dy \(\chi_{2015}(123, \cdot)\) None 0 4
2015.1.ea \(\chi_{2015}(37, \cdot)\) None 0 4
2015.1.ed \(\chi_{2015}(57, \cdot)\) None 0 4
2015.1.ei \(\chi_{2015}(122, \cdot)\) None 0 8
2015.1.ek \(\chi_{2015}(281, \cdot)\) None 0 8
2015.1.em \(\chi_{2015}(233, \cdot)\) None 0 8
2015.1.ep \(\chi_{2015}(157, \cdot)\) None 0 8
2015.1.eq \(\chi_{2015}(109, \cdot)\) None 0 8
2015.1.es \(\chi_{2015}(213, \cdot)\) None 0 8
2015.1.ev \(\chi_{2015}(261, \cdot)\) None 0 8
2015.1.ew \(\chi_{2015}(259, \cdot)\) None 0 8
2015.1.ey \(\chi_{2015}(74, \cdot)\) None 0 8
2015.1.ez \(\chi_{2015}(426, \cdot)\) None 0 8
2015.1.fc \(\chi_{2015}(296, \cdot)\) None 0 8
2015.1.fd \(\chi_{2015}(269, \cdot)\) None 0 8
2015.1.fg \(\chi_{2015}(29, \cdot)\) None 0 8
2015.1.fh \(\chi_{2015}(166, \cdot)\) None 0 8
2015.1.fj \(\chi_{2015}(114, \cdot)\) None 0 8
2015.1.fk \(\chi_{2015}(321, \cdot)\) None 0 8
2015.1.fn \(\chi_{2015}(581, \cdot)\) None 0 8
2015.1.fo \(\chi_{2015}(244, \cdot)\) None 0 8
2015.1.fp \(\chi_{2015}(179, \cdot)\) None 0 8
2015.1.fr \(\chi_{2015}(146, \cdot)\) None 0 8
2015.1.fs \(\chi_{2015}(571, \cdot)\) None 0 8
2015.1.fv \(\chi_{2015}(79, \cdot)\) None 0 8
2015.1.fw \(\chi_{2015}(73, \cdot)\) None 0 16
2015.1.fz \(\chi_{2015}(137, \cdot)\) None 0 16
2015.1.gb \(\chi_{2015}(58, \cdot)\) None 0 16
2015.1.gd \(\chi_{2015}(362, \cdot)\) None 0 16
2015.1.gf \(\chi_{2015}(41, \cdot)\) None 0 16
2015.1.gh \(\chi_{2015}(219, \cdot)\) None 0 16
2015.1.gj \(\chi_{2015}(319, \cdot)\) None 0 16
2015.1.gk \(\chi_{2015}(164, \cdot)\) None 0 16
2015.1.gm \(\chi_{2015}(82, \cdot)\) None 0 16
2015.1.go \(\chi_{2015}(438, \cdot)\) None 0 16
2015.1.gq \(\chi_{2015}(133, \cdot)\) None 0 16
2015.1.gt \(\chi_{2015}(283, \cdot)\) None 0 16
2015.1.gv \(\chi_{2015}(257, \cdot)\) None 0 16
2015.1.gx \(\chi_{2015}(107, \cdot)\) None 0 16
2015.1.gy \(\chi_{2015}(183, \cdot)\) None 0 16
2015.1.hb \(\chi_{2015}(38, \cdot)\) None 0 16
2015.1.hd \(\chi_{2015}(71, \cdot)\) None 0 16
2015.1.hf \(\chi_{2015}(171, \cdot)\) None 0 16
2015.1.hg \(\chi_{2015}(226, \cdot)\) None 0 16
2015.1.hj \(\chi_{2015}(19, \cdot)\) None 0 16
2015.1.hl \(\chi_{2015}(457, \cdot)\) None 0 16
2015.1.hn \(\chi_{2015}(197, \cdot)\) None 0 16
2015.1.hp \(\chi_{2015}(228, \cdot)\) None 0 16
2015.1.hq \(\chi_{2015}(83, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2015))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2015)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(403))\)\(^{\oplus 2}\)