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Properties

Label 2352.2.cm
Level $2352$
Weight $2$
Character orbit 2352.cm
Rep. character $\chi_{2352}(193,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $672$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.cm (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2352, [\chi])\).

Total New Old
Modular forms 5520 672 4848
Cusp forms 5232 672 4560
Eisenstein series 288 0 288

Trace form

\( 672 q + 2 q^{3} + 2 q^{7} + 56 q^{9} + O(q^{10}) \) \( 672 q + 2 q^{3} + 2 q^{7} + 56 q^{9} - 74 q^{19} - 12 q^{23} + 60 q^{25} - 4 q^{27} + 70 q^{31} + 4 q^{33} - 36 q^{35} - 16 q^{39} - 16 q^{41} + 4 q^{43} + 12 q^{47} + 16 q^{49} + 8 q^{53} + 56 q^{55} + 8 q^{57} + 16 q^{59} + 8 q^{61} - 12 q^{63} + 8 q^{65} + 10 q^{67} + 80 q^{71} - 12 q^{73} + 14 q^{75} - 8 q^{77} - 14 q^{79} + 56 q^{81} + 24 q^{83} - 12 q^{87} - 16 q^{89} + 30 q^{91} + 12 q^{95} - 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)