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Properties

Label 2368.1
Level 2368
Weight 1
Dimension 53
Nonzero newspaces 8
Newform subspaces 15
Sturm bound 350208
Trace bound 17

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Defining parameters

Level: \( N \) = \( 2368 = 2^{6} \cdot 37 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 15 \)
Sturm bound: \(350208\)
Trace bound: \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2368))\).

Total New Old
Modular forms 2828 823 2005
Cusp forms 236 53 183
Eisenstein series 2592 770 1822

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 37 4 12 0

Trace form

\( 53 q + 10 q^{5} - 3 q^{9} + O(q^{10}) \) \( 53 q + 10 q^{5} - 3 q^{9} - 2 q^{17} + 8 q^{21} - q^{25} - 2 q^{29} + 6 q^{33} + q^{37} + 6 q^{45} - 7 q^{49} + 2 q^{53} - 10 q^{57} + 2 q^{61} - 6 q^{65} - 4 q^{69} - 10 q^{77} - 3 q^{81} + 12 q^{85} - 6 q^{89} - 4 q^{93} - 6 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2368))\)

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
2368.1.b \(\chi_{2368}(2367, \cdot)\) 2368.1.b.a 1 1
2368.1.b.b 2
2368.1.d \(\chi_{2368}(1407, \cdot)\) None 0 1
2368.1.f \(\chi_{2368}(223, \cdot)\) None 0 1
2368.1.h \(\chi_{2368}(1183, \cdot)\) None 0 1
2368.1.k \(\chi_{2368}(1153, \cdot)\) 2368.1.k.a 2 2
2368.1.k.b 2
2368.1.k.c 2
2368.1.k.d 2
2368.1.k.e 2
2368.1.l \(\chi_{2368}(401, \cdot)\) None 0 2
2368.1.p \(\chi_{2368}(815, \cdot)\) None 0 2
2368.1.q \(\chi_{2368}(591, \cdot)\) None 0 2
2368.1.r \(\chi_{2368}(1585, \cdot)\) None 0 2
2368.1.u \(\chi_{2368}(993, \cdot)\) None 0 2
2368.1.v \(\chi_{2368}(159, \cdot)\) None 0 2
2368.1.x \(\chi_{2368}(1247, \cdot)\) None 0 2
2368.1.z \(\chi_{2368}(63, \cdot)\) 2368.1.z.a 2 2
2368.1.z.b 4
2368.1.z.c 4
2368.1.bb \(\chi_{2368}(767, \cdot)\) 2368.1.bb.a 2 2
2368.1.bd \(\chi_{2368}(295, \cdot)\) None 0 4
2368.1.be \(\chi_{2368}(265, \cdot)\) None 0 4
2368.1.bg \(\chi_{2368}(105, \cdot)\) None 0 4
2368.1.bi \(\chi_{2368}(519, \cdot)\) None 0 4
2368.1.bl \(\chi_{2368}(97, \cdot)\) None 0 4
2368.1.bo \(\chi_{2368}(177, \cdot)\) None 0 4
2368.1.bp \(\chi_{2368}(175, \cdot)\) None 0 4
2368.1.bq \(\chi_{2368}(47, \cdot)\) None 0 4
2368.1.bu \(\chi_{2368}(273, \cdot)\) None 0 4
2368.1.bv \(\chi_{2368}(193, \cdot)\) 2368.1.bv.a 4 4
2368.1.bx \(\chi_{2368}(413, \cdot)\) None 0 8
2368.1.bz \(\chi_{2368}(147, \cdot)\) None 0 8
2368.1.cb \(\chi_{2368}(75, \cdot)\) None 0 8
2368.1.ce \(\chi_{2368}(117, \cdot)\) None 0 8
2368.1.cf \(\chi_{2368}(95, \cdot)\) None 0 6
2368.1.ch \(\chi_{2368}(863, \cdot)\) None 0 6
2368.1.cj \(\chi_{2368}(447, \cdot)\) 2368.1.cj.a 6 6
2368.1.ck \(\chi_{2368}(127, \cdot)\) 2368.1.ck.a 6 6
2368.1.cn \(\chi_{2368}(343, \cdot)\) None 0 8
2368.1.co \(\chi_{2368}(393, \cdot)\) None 0 8
2368.1.cq \(\chi_{2368}(985, \cdot)\) None 0 8
2368.1.cs \(\chi_{2368}(455, \cdot)\) None 0 8
2368.1.cu \(\chi_{2368}(161, \cdot)\) None 0 12
2368.1.cx \(\chi_{2368}(271, \cdot)\) None 0 12
2368.1.cz \(\chi_{2368}(17, \cdot)\) None 0 12
2368.1.da \(\chi_{2368}(209, \cdot)\) None 0 12
2368.1.dd \(\chi_{2368}(559, \cdot)\) None 0 12
2368.1.de \(\chi_{2368}(129, \cdot)\) 2368.1.de.a 12 12
2368.1.dg \(\chi_{2368}(29, \cdot)\) None 0 16
2368.1.di \(\chi_{2368}(11, \cdot)\) None 0 16
2368.1.dk \(\chi_{2368}(195, \cdot)\) None 0 16
2368.1.dn \(\chi_{2368}(45, \cdot)\) None 0 16
2368.1.dp \(\chi_{2368}(153, \cdot)\) None 0 24
2368.1.dq \(\chi_{2368}(7, \cdot)\) None 0 24
2368.1.ds \(\chi_{2368}(151, \cdot)\) None 0 24
2368.1.dv \(\chi_{2368}(57, \cdot)\) None 0 24
2368.1.dx \(\chi_{2368}(3, \cdot)\) None 0 48
2368.1.dy \(\chi_{2368}(5, \cdot)\) None 0 48
2368.1.dz \(\chi_{2368}(13, \cdot)\) None 0 48
2368.1.ed \(\chi_{2368}(83, \cdot)\) None 0 48

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2368))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2368)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(592))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1184))\)\(^{\oplus 2}\)