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Properties

Label 341.1
Level 341
Weight 1
Dimension 14
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 9600
Trace bound 1

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Defining parameters

Level: \( N \) = \( 341 = 11 \cdot 31 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(9600\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(341))\).

Total New Old
Modular forms 316 274 42
Cusp forms 16 14 2
Eisenstein series 300 260 40

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 14 0 0 0

Trace form

\( 14 q - 2 q^{3} - q^{4} - 2 q^{5} - 3 q^{9} + O(q^{10}) \) \( 14 q - 2 q^{3} - q^{4} - 2 q^{5} - 3 q^{9} - q^{11} - 2 q^{12} - 4 q^{15} - q^{16} - 2 q^{20} - 2 q^{23} - 3 q^{25} + 11 q^{27} - q^{31} - 2 q^{33} - 3 q^{36} + 13 q^{37} - q^{44} - 6 q^{45} - 2 q^{47} - 2 q^{48} - q^{49} - 2 q^{53} - 2 q^{55} - 2 q^{59} - 4 q^{60} - q^{64} - 2 q^{67} - 4 q^{69} - 2 q^{71} + 9 q^{75} + 13 q^{80} - 5 q^{81} - 2 q^{89} - 2 q^{92} - 2 q^{93} - 2 q^{97} - 3 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(341))\)

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
341.1.c \(\chi_{341}(32, \cdot)\) None 0 1
341.1.d \(\chi_{341}(309, \cdot)\) None 0 1
341.1.l \(\chi_{341}(87, \cdot)\) 341.1.l.a 2 2
341.1.n \(\chi_{341}(243, \cdot)\) None 0 2
341.1.o \(\chi_{341}(35, \cdot)\) None 0 4
341.1.q \(\chi_{341}(58, \cdot)\) None 0 4
341.1.r \(\chi_{341}(27, \cdot)\) None 0 4
341.1.s \(\chi_{341}(170, \cdot)\) None 0 4
341.1.t \(\chi_{341}(92, \cdot)\) None 0 4
341.1.u \(\chi_{341}(23, \cdot)\) None 0 4
341.1.w \(\chi_{341}(63, \cdot)\) None 0 4
341.1.x \(\chi_{341}(95, \cdot)\) None 0 4
341.1.y \(\chi_{341}(2, \cdot)\) None 0 4
341.1.z \(\chi_{341}(109, \cdot)\) 341.1.z.a 4 4
341.1.be \(\chi_{341}(194, \cdot)\) None 0 4
341.1.bf \(\chi_{341}(15, \cdot)\) None 0 4
341.1.bn \(\chi_{341}(18, \cdot)\) None 0 8
341.1.bo \(\chi_{341}(12, \cdot)\) None 0 8
341.1.bp \(\chi_{341}(26, \cdot)\) None 0 8
341.1.bq \(\chi_{341}(137, \cdot)\) None 0 8
341.1.br \(\chi_{341}(3, \cdot)\) None 0 8
341.1.bs \(\chi_{341}(48, \cdot)\) None 0 8
341.1.bt \(\chi_{341}(40, \cdot)\) None 0 8
341.1.by \(\chi_{341}(10, \cdot)\) 341.1.by.a 8 8
341.1.bz \(\chi_{341}(7, \cdot)\) None 0 8
341.1.ca \(\chi_{341}(173, \cdot)\) None 0 8
341.1.cb \(\chi_{341}(118, \cdot)\) None 0 8
341.1.cd \(\chi_{341}(42, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(341))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(341)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)