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Properties

Label 364.1
Level 364
Weight 1
Dimension 6
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 8064
Trace bound 1

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Defining parameters

Level: \( N \) = \( 364 = 2^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(8064\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(364))\).

Total New Old
Modular forms 370 118 252
Cusp forms 10 6 4
Eisenstein series 360 112 248

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6 q - 2 q^{4} + O(q^{10}) \) \( 6 q - 2 q^{4} + 4 q^{13} - 2 q^{14} - 2 q^{16} + 2 q^{17} - 4 q^{22} - 2 q^{23} - 2 q^{25} - 6 q^{29} - 2 q^{35} + 4 q^{36} + 2 q^{38} - 2 q^{43} - 2 q^{52} - 2 q^{56} + 2 q^{61} + 8 q^{62} + 4 q^{64} - 2 q^{65} + 2 q^{68} - 4 q^{77} - 2 q^{79} + 2 q^{88} + 2 q^{91} + 2 q^{94} + 2 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(364))\)

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
364.1.b \(\chi_{364}(209, \cdot)\) None 0 1
364.1.c \(\chi_{364}(155, \cdot)\) None 0 1
364.1.d \(\chi_{364}(181, \cdot)\) 364.1.d.a 1 1
364.1.d.b 1
364.1.e \(\chi_{364}(183, \cdot)\) None 0 1
364.1.o \(\chi_{364}(57, \cdot)\) None 0 2
364.1.p \(\chi_{364}(83, \cdot)\) None 0 2
364.1.q \(\chi_{364}(191, \cdot)\) None 0 2
364.1.r \(\chi_{364}(101, \cdot)\) None 0 2
364.1.s \(\chi_{364}(179, \cdot)\) None 0 2
364.1.t \(\chi_{364}(61, \cdot)\) None 0 2
364.1.bd \(\chi_{364}(43, \cdot)\) None 0 2
364.1.be \(\chi_{364}(237, \cdot)\) None 0 2
364.1.bf \(\chi_{364}(79, \cdot)\) None 0 2
364.1.bg \(\chi_{364}(129, \cdot)\) None 0 2
364.1.bh \(\chi_{364}(17, \cdot)\) None 0 2
364.1.bi \(\chi_{364}(107, \cdot)\) None 0 2
364.1.bj \(\chi_{364}(269, \cdot)\) None 0 2
364.1.bk \(\chi_{364}(23, \cdot)\) None 0 2
364.1.bl \(\chi_{364}(51, \cdot)\) 364.1.bl.a 2 2
364.1.bl.b 2
364.1.bm \(\chi_{364}(157, \cdot)\) None 0 2
364.1.bn \(\chi_{364}(211, \cdot)\) None 0 2
364.1.bo \(\chi_{364}(69, \cdot)\) None 0 2
364.1.bu \(\chi_{364}(37, \cdot)\) None 0 4
364.1.bv \(\chi_{364}(111, \cdot)\) None 0 4
364.1.bw \(\chi_{364}(31, \cdot)\) None 0 4
364.1.bx \(\chi_{364}(85, \cdot)\) None 0 4
364.1.by \(\chi_{364}(109, \cdot)\) None 0 4
364.1.bz \(\chi_{364}(59, \cdot)\) None 0 4
364.1.cg \(\chi_{364}(19, \cdot)\) None 0 4
364.1.ch \(\chi_{364}(149, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(364))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(364)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)