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Properties

Label 1100.2.bm
Level $1100$
Weight $2$
Character orbit 1100.bm
Rep. character $\chi_{1100}(89,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $104$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1100.bm (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1100, [\chi])\).

Total New Old
Modular forms 744 104 640
Cusp forms 696 104 592
Eisenstein series 48 0 48

Trace form

\( 104 q - 4 q^{5} + 28 q^{9} + O(q^{10}) \) \( 104 q - 4 q^{5} + 28 q^{9} - 2 q^{11} + 29 q^{15} + 12 q^{21} + 20 q^{23} + 12 q^{25} - 15 q^{27} + 4 q^{29} + 6 q^{31} + 2 q^{35} + 20 q^{37} - 24 q^{39} + 8 q^{41} - 20 q^{45} - 50 q^{47} - 136 q^{49} - 4 q^{51} - 60 q^{53} - 3 q^{55} - 9 q^{59} - 40 q^{63} + 58 q^{65} - 15 q^{67} + 47 q^{69} - 28 q^{71} + 120 q^{73} - 47 q^{75} + 16 q^{79} - 37 q^{81} + 40 q^{83} + 18 q^{85} + 150 q^{87} + 34 q^{89} - 60 q^{91} - 48 q^{95} - 30 q^{97} - 14 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1100, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1100, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)