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Properties

Label 273.1
Level 273
Weight 1
Dimension 28
Nonzero newspaces 7
Newform subspaces 10
Sturm bound 5376
Trace bound 7

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Defining parameters

Level: \( N \) = \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 10 \)
Sturm bound: \(5376\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(273))\).

Total New Old
Modular forms 318 140 178
Cusp forms 30 28 2
Eisenstein series 288 112 176

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 8 0 0

Trace form

\( 28 q - 4 q^{6} - 6 q^{9} + O(q^{10}) \) \( 28 q - 4 q^{6} - 6 q^{9} - 2 q^{10} - 4 q^{12} - 8 q^{13} - 4 q^{15} - 6 q^{16} - 4 q^{19} - 2 q^{21} + 2 q^{24} - 2 q^{28} + 8 q^{34} - 2 q^{37} - 4 q^{39} + 4 q^{40} + 2 q^{42} - 12 q^{43} + 2 q^{46} - 2 q^{49} + 4 q^{51} - 4 q^{52} - 2 q^{54} - 4 q^{57} + 2 q^{58} - 4 q^{63} - 8 q^{64} - 4 q^{67} + 4 q^{69} - 8 q^{70} + 4 q^{73} + 8 q^{75} + 8 q^{76} + 4 q^{78} - 4 q^{79} + 10 q^{81} - 2 q^{82} + 10 q^{84} - 4 q^{85} - 2 q^{87} + 8 q^{90} + 8 q^{91} + 8 q^{93} - 2 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(273))\)

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
273.1.b \(\chi_{273}(92, \cdot)\) None 0 1
273.1.d \(\chi_{273}(181, \cdot)\) None 0 1
273.1.f \(\chi_{273}(118, \cdot)\) None 0 1
273.1.h \(\chi_{273}(155, \cdot)\) None 0 1
273.1.m \(\chi_{273}(148, \cdot)\) None 0 2
273.1.o \(\chi_{273}(83, \cdot)\) 273.1.o.a 2 2
273.1.o.b 2
273.1.q \(\chi_{273}(166, \cdot)\) None 0 2
273.1.s \(\chi_{273}(74, \cdot)\) 273.1.s.a 2 2
273.1.s.b 4
273.1.v \(\chi_{273}(55, \cdot)\) None 0 2
273.1.w \(\chi_{273}(116, \cdot)\) None 0 2
273.1.x \(\chi_{273}(179, \cdot)\) 273.1.x.a 2 2
273.1.z \(\chi_{273}(61, \cdot)\) None 0 2
273.1.bb \(\chi_{273}(40, \cdot)\) None 0 2
273.1.bc \(\chi_{273}(134, \cdot)\) None 0 2
273.1.be \(\chi_{273}(29, \cdot)\) None 0 2
273.1.bg \(\chi_{273}(10, \cdot)\) None 0 2
273.1.bi \(\chi_{273}(103, \cdot)\) None 0 2
273.1.bk \(\chi_{273}(53, \cdot)\) None 0 2
273.1.bm \(\chi_{273}(191, \cdot)\) 273.1.bm.a 2 2
273.1.bm.b 4
273.1.bo \(\chi_{273}(160, \cdot)\) None 0 2
273.1.bp \(\chi_{273}(23, \cdot)\) 273.1.bp.a 2 2
273.1.bq \(\chi_{273}(178, \cdot)\) None 0 2
273.1.bs \(\chi_{273}(59, \cdot)\) 273.1.bs.a 4 4
273.1.bu \(\chi_{273}(37, \cdot)\) None 0 4
273.1.bx \(\chi_{273}(58, \cdot)\) None 0 4
273.1.ca \(\chi_{273}(20, \cdot)\) None 0 4
273.1.cb \(\chi_{273}(5, \cdot)\) None 0 4
273.1.ce \(\chi_{273}(85, \cdot)\) None 0 4
273.1.cf \(\chi_{273}(109, \cdot)\) None 0 4
273.1.ch \(\chi_{273}(80, \cdot)\) 273.1.ch.a 4 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(273))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(273)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 1}\)