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Properties

Label 2224.1
Level 2224
Weight 1
Dimension 4
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 309120
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2224 = 2^{4} \cdot 139 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(309120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2224))\).

Total New Old
Modular forms 2106 621 1485
Cusp forms 174 4 170
Eisenstein series 1932 617 1315

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

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

Trace form

\( 4 q - q^{5} + q^{7} + 4 q^{9} + O(q^{10}) \) \( 4 q - q^{5} + q^{7} + 4 q^{9} + q^{11} - q^{13} + 3 q^{25} - q^{29} + q^{31} + 2 q^{35} - q^{37} - q^{41} - q^{45} + q^{47} + 3 q^{49} + 2 q^{55} + q^{63} - 2 q^{65} + q^{67} + q^{71} - 2 q^{77} + q^{79} + 4 q^{81} + q^{83} - q^{89} + 2 q^{91} + q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2224))\)

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
2224.1.d \(\chi_{2224}(1391, \cdot)\) None 0 1
2224.1.e \(\chi_{2224}(833, \cdot)\) 2224.1.e.a 1 1
2224.1.e.b 3
2224.1.f \(\chi_{2224}(279, \cdot)\) None 0 1
2224.1.g \(\chi_{2224}(1945, \cdot)\) None 0 1
2224.1.j \(\chi_{2224}(277, \cdot)\) None 0 2
2224.1.l \(\chi_{2224}(835, \cdot)\) None 0 2
2224.1.o \(\chi_{2224}(1209, \cdot)\) None 0 2
2224.1.p \(\chi_{2224}(791, \cdot)\) None 0 2
2224.1.q \(\chi_{2224}(97, \cdot)\) None 0 2
2224.1.r \(\chi_{2224}(1903, \cdot)\) None 0 2
2224.1.v \(\chi_{2224}(235, \cdot)\) None 0 4
2224.1.x \(\chi_{2224}(653, \cdot)\) None 0 4
2224.1.ba \(\chi_{2224}(105, \cdot)\) None 0 22
2224.1.bb \(\chi_{2224}(55, \cdot)\) None 0 22
2224.1.bc \(\chi_{2224}(33, \cdot)\) None 0 22
2224.1.bd \(\chi_{2224}(63, \cdot)\) None 0 22
2224.1.bi \(\chi_{2224}(91, \cdot)\) None 0 44
2224.1.bk \(\chi_{2224}(133, \cdot)\) None 0 44
2224.1.bn \(\chi_{2224}(31, \cdot)\) None 0 44
2224.1.bo \(\chi_{2224}(17, \cdot)\) None 0 44
2224.1.bp \(\chi_{2224}(7, \cdot)\) None 0 44
2224.1.bq \(\chi_{2224}(73, \cdot)\) None 0 44
2224.1.bs \(\chi_{2224}(21, \cdot)\) None 0 88
2224.1.bu \(\chi_{2224}(11, \cdot)\) None 0 88

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2224))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2224)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(139))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(556))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1112))\)\(^{\oplus 2}\)