Properties

Label 2015.1
Level 2015
Weight 1
Dimension 52
Nonzero newspaces 3
Newforms 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: \( 3 \)
Newforms: \( 11 \)
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

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

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

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