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Properties

Label 2156.2.bh
Level $2156$
Weight $2$
Character orbit 2156.bh
Rep. character $\chi_{2156}(221,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $552$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2156.bh (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2156, [\chi])\).

Total New Old
Modular forms 4104 552 3552
Cusp forms 3960 552 3408
Eisenstein series 144 0 144

Trace form

\( 552 q - 2 q^{3} - 4 q^{5} - 6 q^{7} + 76 q^{9} + O(q^{10}) \) \( 552 q - 2 q^{3} - 4 q^{5} - 6 q^{7} + 76 q^{9} + 12 q^{15} - 6 q^{17} + 2 q^{19} + 18 q^{21} + 42 q^{25} - 32 q^{27} + 28 q^{29} + 10 q^{31} - 4 q^{33} + 26 q^{35} + 26 q^{37} + 60 q^{39} + 32 q^{41} - 44 q^{43} - 14 q^{45} + 122 q^{47} + 12 q^{51} + 26 q^{53} - 50 q^{57} + 52 q^{59} + 10 q^{61} - 40 q^{63} - 14 q^{65} + 8 q^{67} + 60 q^{69} - 22 q^{71} + 34 q^{73} + 178 q^{75} + 2 q^{77} + 16 q^{79} + 82 q^{81} - 166 q^{83} + 112 q^{85} - 42 q^{87} - 30 q^{89} - 58 q^{91} - 414 q^{93} + 4 q^{95} - 140 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2156, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2156, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2156, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1078, [\chi])\)\(^{\oplus 2}\)