Properties

Label 1150.2.b
Level $1150$
Weight $2$
Character orbit 1150.b
Rep. character $\chi_{1150}(599,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $10$
Sturm bound $360$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1150.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(360\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1150, [\chi])\).

Total New Old
Modular forms 192 32 160
Cusp forms 168 32 136
Eisenstein series 24 0 24

Trace form

\( 32 q - 32 q^{4} - 4 q^{6} - 44 q^{9} + O(q^{10}) \) \( 32 q - 32 q^{4} - 4 q^{6} - 44 q^{9} + 16 q^{11} + 32 q^{16} + 8 q^{19} - 16 q^{21} + 4 q^{24} - 24 q^{26} - 8 q^{31} + 20 q^{34} + 44 q^{36} + 16 q^{39} - 44 q^{41} - 16 q^{44} - 4 q^{46} - 16 q^{49} - 44 q^{51} + 52 q^{54} + 40 q^{59} - 60 q^{61} - 32 q^{64} - 44 q^{66} + 8 q^{69} - 24 q^{71} + 12 q^{74} - 8 q^{76} - 24 q^{79} + 48 q^{81} + 16 q^{84} + 20 q^{86} + 60 q^{89} + 8 q^{91} + 16 q^{94} - 4 q^{96} - 68 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1150, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1150.2.b.a 1150.b 5.b $2$ $9.183$ \(\Q(\sqrt{-1}) \) None 1150.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-4iq^{7}+\cdots\)
1150.2.b.b 1150.b 5.b $2$ $9.183$ \(\Q(\sqrt{-1}) \) None 1150.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{7}+\cdots\)
1150.2.b.c 1150.b 5.b $2$ $9.183$ \(\Q(\sqrt{-1}) \) None 1150.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+3q^{9}+\cdots\)
1150.2.b.d 1150.b 5.b $2$ $9.183$ \(\Q(\sqrt{-1}) \) None 46.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}-4iq^{7}+iq^{8}+3q^{9}+\cdots\)
1150.2.b.e 1150.b 5.b $2$ $9.183$ \(\Q(\sqrt{-1}) \) None 1150.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}-iq^{7}+\cdots\)
1150.2.b.f 1150.b 5.b $4$ $9.183$ \(\Q(i, \sqrt{13})\) None 230.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-q^{4}+(-2+\cdots)q^{6}+\cdots\)
1150.2.b.g 1150.b 5.b $4$ $9.183$ \(\Q(i, \sqrt{21})\) None 230.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(1-\beta _{3})q^{6}+\cdots\)
1150.2.b.h 1150.b 5.b $4$ $9.183$ \(\Q(i, \sqrt{17})\) None 1150.2.a.k \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(1-\beta _{3})q^{6}+\cdots\)
1150.2.b.i 1150.b 5.b $4$ $9.183$ \(\Q(i, \sqrt{5})\) None 230.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{2}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1150.2.b.j 1150.b 5.b $6$ $9.183$ 6.0.77580864.1 None 230.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{3}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1150, [\chi])\) into lower level spaces

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