Properties

Label 1100.2.u
Level $1100$
Weight $2$
Character orbit 1100.u
Rep. character $\chi_{1100}(229,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $120$
Sturm bound $360$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1100.u (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
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 744 120 624
Cusp forms 696 120 576
Eisenstein series 48 0 48

Trace form

\( 120 q - 4 q^{5} + 5 q^{7} - 118 q^{9} + O(q^{10}) \) \( 120 q - 4 q^{5} + 5 q^{7} - 118 q^{9} + 3 q^{11} + 4 q^{15} - 5 q^{17} - 6 q^{19} + 8 q^{21} + 22 q^{25} - 12 q^{29} + 7 q^{31} + 15 q^{33} - 8 q^{35} - 35 q^{37} - 30 q^{39} + 19 q^{41} + 30 q^{45} + 27 q^{49} + 8 q^{51} - 15 q^{53} - 18 q^{55} - 20 q^{57} - 6 q^{59} - 68 q^{61} - 15 q^{63} - 7 q^{65} + 55 q^{67} - 6 q^{69} - 35 q^{71} - 15 q^{73} - 67 q^{75} + 15 q^{77} + 8 q^{79} + 92 q^{81} + 50 q^{83} + 33 q^{85} + 10 q^{89} - 36 q^{91} + 40 q^{93} - 53 q^{95} - 59 q^{99} + O(q^{100}) \)

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

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