Properties

Label 275.1
Level 275
Weight 1
Dimension 9
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 6000
Trace bound 3

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Defining parameters

Level: \( N \) = \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(6000\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(275))\).

Total New Old
Modular forms 291 194 97
Cusp forms 11 9 2
Eisenstein series 280 185 95

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 9 0 0 0

Trace form

\( 9 q - 2 q^{3} + q^{4} - 5 q^{9} + O(q^{10}) \) \( 9 q - 2 q^{3} + q^{4} - 5 q^{9} - q^{11} - 2 q^{12} - 2 q^{15} - q^{16} - 2 q^{20} - 2 q^{23} + 8 q^{25} + 6 q^{27} - 2 q^{31} - 2 q^{33} - 3 q^{36} - 2 q^{37} - 3 q^{44} - 2 q^{45} - 2 q^{47} - 2 q^{48} + q^{49} - 2 q^{53} - 2 q^{55} + 4 q^{59} + 8 q^{60} + q^{64} - 2 q^{67} - 4 q^{69} - 2 q^{71} - 2 q^{75} - 5 q^{81} + 2 q^{89} + 8 q^{92} + 6 q^{93} - 2 q^{97} + 9 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(275))\)

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
275.1.c \(\chi_{275}(76, \cdot)\) 275.1.c.a 1 1
275.1.d \(\chi_{275}(274, \cdot)\) None 0 1
275.1.f \(\chi_{275}(232, \cdot)\) None 0 2
275.1.m \(\chi_{275}(41, \cdot)\) None 0 4
275.1.o \(\chi_{275}(79, \cdot)\) None 0 4
275.1.p \(\chi_{275}(39, \cdot)\) None 0 4
275.1.q \(\chi_{275}(24, \cdot)\) None 0 4
275.1.r \(\chi_{275}(19, \cdot)\) None 0 4
275.1.s \(\chi_{275}(54, \cdot)\) 275.1.s.a 4 4
275.1.u \(\chi_{275}(61, \cdot)\) None 0 4
275.1.v \(\chi_{275}(21, \cdot)\) 275.1.v.a 4 4
275.1.w \(\chi_{275}(116, \cdot)\) None 0 4
275.1.x \(\chi_{275}(51, \cdot)\) None 0 4
275.1.bc \(\chi_{275}(6, \cdot)\) None 0 4
275.1.bd \(\chi_{275}(139, \cdot)\) None 0 4
275.1.be \(\chi_{275}(42, \cdot)\) None 0 8
275.1.bh \(\chi_{275}(37, \cdot)\) None 0 8
275.1.bi \(\chi_{275}(12, \cdot)\) None 0 8
275.1.bj \(\chi_{275}(38, \cdot)\) None 0 8
275.1.bk \(\chi_{275}(82, \cdot)\) None 0 8
275.1.bp \(\chi_{275}(3, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(275))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(275)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)