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Properties

Label 1100.2.cb
Level $1100$
Weight $2$
Character orbit 1100.cb
Rep. character $\chi_{1100}(49,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $72$
Newform subspaces $4$
Sturm bound $360$
Trace bound $21$

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Defining parameters

Level: \( N \) \(=\) \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1100.cb (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 4 \)
Sturm bound: \(360\)
Trace bound: \(21\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 792 72 720
Cusp forms 648 72 576
Eisenstein series 144 0 144

Trace form

\( 72 q + 4 q^{9} + O(q^{10}) \) \( 72 q + 4 q^{9} + 2 q^{11} - 12 q^{19} + 24 q^{21} + 20 q^{29} + 34 q^{31} - 4 q^{39} - 16 q^{41} + 84 q^{49} - 28 q^{51} - 10 q^{59} + 22 q^{61} + 70 q^{69} - 14 q^{71} + 96 q^{79} - 30 q^{81} - 4 q^{89} + 14 q^{91} - 176 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1100.2.cb.a 1100.cb 55.j $8$ $8.784$ \(\Q(\zeta_{20})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(2\zeta_{20}+\zeta_{20}^{5}-\zeta_{20}^{7})q^{3}+(2\zeta_{20}+\cdots)q^{7}+\cdots\)
1100.2.cb.b 1100.cb 55.j $16$ $8.784$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\beta _{2}-\beta _{6}-\beta _{10}-\beta _{12}-\beta _{13}+\beta _{14}+\cdots)q^{3}+\cdots\)
1100.2.cb.c 1100.cb 55.j $16$ $8.784$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(2\beta _{1}-\beta _{2}+\beta _{7}-\beta _{9}-\beta _{11}+\beta _{13}+\cdots)q^{3}+\cdots\)
1100.2.cb.d 1100.cb 55.j $32$ $8.784$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$

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

\( S_{2}^{\mathrm{old}}(1100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)