Properties

Label 2842.2.cd
Level $2842$
Weight $2$
Character orbit 2842.cd
Rep. character $\chi_{2842}(97,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $1200$
Sturm bound $840$

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Defining parameters

Level: \( N \) \(=\) \( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2842.cd (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 203 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2842, [\chi])\).

Total New Old
Modular forms 5232 1200 4032
Cusp forms 4848 1200 3648
Eisenstein series 384 0 384

Trace form

\( 1200 q + O(q^{10}) \) \( 1200 q + 16 q^{11} + 16 q^{15} + 200 q^{16} + 56 q^{22} - 280 q^{25} + 88 q^{29} - 160 q^{36} + 8 q^{37} - 136 q^{39} + 16 q^{43} - 16 q^{44} - 40 q^{46} + 8 q^{50} - 112 q^{51} - 136 q^{53} + 8 q^{58} + 16 q^{60} + 104 q^{65} + 112 q^{67} - 168 q^{71} + 120 q^{74} - 160 q^{78} + 64 q^{79} + 616 q^{81} - 376 q^{85} - 168 q^{92} + 376 q^{95} + 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2842, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2842, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2842, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(203, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(406, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1421, [\chi])\)\(^{\oplus 2}\)