Properties

Label 1150.4.b
Level $1150$
Weight $4$
Character orbit 1150.b
Rep. character $\chi_{1150}(599,\cdot)$
Character field $\Q$
Dimension $100$
Newform subspaces $19$
Sturm bound $720$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1150.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(720\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1150, [\chi])\).

Total New Old
Modular forms 552 100 452
Cusp forms 528 100 428
Eisenstein series 24 0 24

Trace form

\( 100 q - 400 q^{4} + 24 q^{6} - 808 q^{9} + O(q^{10}) \) \( 100 q - 400 q^{4} + 24 q^{6} - 808 q^{9} - 32 q^{11} + 1600 q^{16} - 144 q^{19} + 448 q^{21} - 96 q^{24} + 384 q^{26} - 944 q^{29} - 872 q^{31} + 680 q^{34} + 3232 q^{36} - 1168 q^{39} + 756 q^{41} + 128 q^{44} + 184 q^{46} - 4564 q^{49} + 2524 q^{51} - 216 q^{54} - 2296 q^{59} - 932 q^{61} - 6400 q^{64} - 1064 q^{66} - 552 q^{69} - 1576 q^{71} + 2616 q^{74} + 576 q^{76} + 4600 q^{79} + 11060 q^{81} - 1792 q^{84} - 2360 q^{86} + 6764 q^{89} - 6600 q^{91} - 480 q^{94} + 384 q^{96} - 3140 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1150, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1150.4.b.a $2$ $67.852$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}+9iq^{3}-4q^{4}-18q^{6}+2iq^{7}+\cdots\)
1150.4.b.b $2$ $67.852$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}+7iq^{3}-4q^{4}-14q^{6}-20iq^{7}+\cdots\)
1150.4.b.c $2$ $67.852$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}+4iq^{3}-4q^{4}-8q^{6}-3iq^{7}+\cdots\)
1150.4.b.d $2$ $67.852$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}+iq^{3}-4q^{4}-2q^{6}-2^{5}iq^{7}+\cdots\)
1150.4.b.e $2$ $67.852$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2iq^{2}+iq^{3}-4q^{4}+2q^{6}-12iq^{7}+\cdots\)
1150.4.b.f $2$ $67.852$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2iq^{2}+iq^{3}-4q^{4}+2q^{6}+18iq^{7}+\cdots\)
1150.4.b.g $2$ $67.852$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2iq^{2}+2iq^{3}-4q^{4}+4q^{6}-21iq^{7}+\cdots\)
1150.4.b.h $2$ $67.852$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2iq^{2}+5iq^{3}-4q^{4}+10q^{6}+12iq^{7}+\cdots\)
1150.4.b.i $4$ $67.852$ \(\Q(i, \sqrt{41})\) None \(0\) \(0\) \(0\) \(0\) \(q-2\beta _{2}q^{2}+(-3\beta _{1}-\beta _{2})q^{3}-4q^{4}+\cdots\)
1150.4.b.j $4$ $67.852$ \(\Q(i, \sqrt{73})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-4q^{4}+(4+\cdots)q^{6}+\cdots\)
1150.4.b.k $4$ $67.852$ \(\Q(i, \sqrt{73})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-4q^{4}+(4+\cdots)q^{6}+\cdots\)
1150.4.b.l $6$ $67.852$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{2}q^{2}+\beta _{1}q^{3}-4q^{4}-2\beta _{3}q^{6}+\cdots\)
1150.4.b.m $8$ $67.852$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-4q^{4}+(2+\cdots)q^{6}+\cdots\)
1150.4.b.n $8$ $67.852$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-4q^{4}+(2+\cdots)q^{6}+\cdots\)
1150.4.b.o $8$ $67.852$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{6}q^{2}+(\beta _{1}-3\beta _{6})q^{3}-4q^{4}+(6+\cdots)q^{6}+\cdots\)
1150.4.b.p $10$ $67.852$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-2\beta _{5}q^{2}+(-2\beta _{5}+\beta _{8})q^{3}-4q^{4}+\cdots\)
1150.4.b.q $10$ $67.852$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-2\beta _{6}q^{2}+\beta _{1}q^{3}-4q^{4}+2\beta _{2}q^{6}+\cdots\)
1150.4.b.r $10$ $67.852$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-4q^{4}+(2+\cdots)q^{6}+\cdots\)
1150.4.b.s $12$ $67.852$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{7}q^{2}+(\beta _{1}+\beta _{7})q^{3}-4q^{4}+(-2+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(1150, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1150, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 2}\)