Properties

Label 1100.6.b
Level $1100$
Weight $6$
Character orbit 1100.b
Rep. character $\chi_{1100}(749,\cdot)$
Character field $\Q$
Dimension $74$
Newform subspaces $9$
Sturm bound $1080$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1100.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(1080\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1100, [\chi])\).

Total New Old
Modular forms 918 74 844
Cusp forms 882 74 808
Eisenstein series 36 0 36

Trace form

\( 74 q - 4972 q^{9} + O(q^{10}) \) \( 74 q - 4972 q^{9} - 242 q^{11} - 1220 q^{19} - 608 q^{21} + 21004 q^{29} - 10854 q^{31} + 25196 q^{39} + 64908 q^{41} - 186366 q^{49} + 92716 q^{51} - 122934 q^{59} - 40560 q^{61} - 248638 q^{69} + 235342 q^{71} - 56984 q^{79} + 445258 q^{81} + 320274 q^{89} + 125900 q^{91} + 173756 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(1100, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1100.6.b.a 1100.b 5.b $2$ $176.422$ \(\Q(\sqrt{-1}) \) None 44.6.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+7iq^{3}+50iq^{7}+194q^{9}+11^{2}q^{11}+\cdots\)
1100.6.b.b 1100.b 5.b $4$ $176.422$ \(\Q(i, \sqrt{1761})\) None 220.6.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-5\beta _{2})q^{3}+(5\beta _{1}+34\beta _{2})q^{7}+\cdots\)
1100.6.b.c 1100.b 5.b $4$ $176.422$ \(\Q(i, \sqrt{31})\) None 44.6.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-3\beta _{1}+\beta _{3})q^{3}+(-134\beta _{1}+3\beta _{3})q^{7}+\cdots\)
1100.6.b.d 1100.b 5.b $6$ $176.422$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 220.6.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{3}+(-24\beta _{3}+7\beta _{4}+2\beta _{5})q^{7}+\cdots\)
1100.6.b.e 1100.b 5.b $8$ $176.422$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 220.6.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+(-6\beta _{2}+\beta _{4})q^{7}+(-58+\cdots)q^{9}+\cdots\)
1100.6.b.f 1100.b 5.b $8$ $176.422$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 220.6.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(3\beta _{1}-\beta _{2}-\beta _{4})q^{7}+(-58+\cdots)q^{9}+\cdots\)
1100.6.b.g 1100.b 5.b $10$ $176.422$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 220.6.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{3}+(-\beta _{5}+2\beta _{6}+\beta _{8})q^{7}+(-94+\cdots)q^{9}+\cdots\)
1100.6.b.h 1100.b 5.b $16$ $176.422$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 1100.6.a.i \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{8}q^{3}+(-2\beta _{8}+4\beta _{9}-\beta _{10})q^{7}+\cdots\)
1100.6.b.i 1100.b 5.b $16$ $176.422$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 1100.6.a.h \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{8}+\beta _{9})q^{3}+(-2\beta _{9}+\beta _{10})q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(1100, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(1100, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)