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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1150.2.b.a \(2\) \(9.183\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-4iq^{7}+\cdots\)
1150.2.b.b \(2\) \(9.183\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{7}+\cdots\)
1150.2.b.c \(2\) \(9.183\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+3q^{9}+\cdots\)
1150.2.b.d \(2\) \(9.183\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}-4iq^{7}+iq^{8}+3q^{9}+\cdots\)
1150.2.b.e \(2\) \(9.183\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}-iq^{7}+\cdots\)
1150.2.b.f \(4\) \(9.183\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-q^{4}+(-2+\cdots)q^{6}+\cdots\)
1150.2.b.g \(4\) \(9.183\) \(\Q(i, \sqrt{21})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(1-\beta _{3})q^{6}+\cdots\)
1150.2.b.h \(4\) \(9.183\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(1-\beta _{3})q^{6}+\cdots\)
1150.2.b.i \(4\) \(9.183\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{2}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1150.2.b.j \(6\) \(9.183\) 6.0.77580864.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{3}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)

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

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