Properties

Label 363.3.b
Level $363$
Weight $3$
Character orbit 363.b
Rep. character $\chi_{363}(122,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $14$
Sturm bound $132$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 363.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 14 \)
Sturm bound: \(132\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(363, [\chi])\).

Total New Old
Modular forms 100 82 18
Cusp forms 76 64 12
Eisenstein series 24 18 6

Trace form

\( 64 q - 108 q^{4} + 2 q^{6} + 12 q^{7} - 16 q^{9} + O(q^{10}) \) \( 64 q - 108 q^{4} + 2 q^{6} + 12 q^{7} - 16 q^{9} - 36 q^{10} + 10 q^{12} + 10 q^{15} + 172 q^{16} - 38 q^{18} + 48 q^{19} + 86 q^{21} - 24 q^{24} - 204 q^{25} - 66 q^{27} - 48 q^{28} - 142 q^{30} + 36 q^{31} - 36 q^{34} + 262 q^{36} - 28 q^{37} + 32 q^{39} + 168 q^{40} + 108 q^{42} - 180 q^{43} - 34 q^{45} + 132 q^{46} + 10 q^{48} + 132 q^{49} - 214 q^{51} + 192 q^{52} + 176 q^{54} - 108 q^{57} - 532 q^{58} - 352 q^{60} - 14 q^{63} - 168 q^{64} - 28 q^{67} + 358 q^{69} + 324 q^{70} - 72 q^{72} + 432 q^{73} + 170 q^{75} - 264 q^{76} + 232 q^{78} + 156 q^{79} - 208 q^{81} + 168 q^{82} - 416 q^{84} - 108 q^{85} + 252 q^{87} - 410 q^{90} - 236 q^{91} - 54 q^{93} + 312 q^{94} - 272 q^{96} - 484 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(363, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
363.3.b.a \(1\) \(9.891\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(-11\) \(q-3q^{3}+4q^{4}-11q^{7}+9q^{9}-12q^{12}+\cdots\)
363.3.b.b \(1\) \(9.891\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(11\) \(q-3q^{3}+4q^{4}+11q^{7}+9q^{9}-12q^{12}+\cdots\)
363.3.b.c \(2\) \(9.891\) \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) \(0\) \(5\) \(0\) \(0\) \(q+(3-\beta )q^{3}+4q^{4}+(-3+6\beta )q^{5}+\cdots\)
363.3.b.d \(2\) \(9.891\) \(\Q(\sqrt{-11}) \) None \(0\) \(6\) \(0\) \(16\) \(q-\beta q^{2}+3q^{3}-7q^{4}-2\beta q^{5}-3\beta q^{6}+\cdots\)
363.3.b.e \(2\) \(9.891\) \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(6\) \(0\) \(0\) \(q+3q^{3}+4q^{4}-5\beta q^{7}+9q^{9}+12q^{12}+\cdots\)
363.3.b.f \(4\) \(9.891\) \(\Q(i, \sqrt{5})\) None \(0\) \(-8\) \(0\) \(-22\) \(q-\beta _{3}q^{2}+(-2-2\beta _{1}-\beta _{3})q^{3}+3q^{4}+\cdots\)
363.3.b.g \(4\) \(9.891\) \(\Q(i, \sqrt{5})\) None \(0\) \(-8\) \(0\) \(22\) \(q+\beta _{3}q^{2}+(-2-2\beta _{1}-\beta _{3})q^{3}+3q^{4}+\cdots\)
363.3.b.h \(4\) \(9.891\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-5\) \(0\) \(-4\) \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(-1+\beta _{2}+\cdots)q^{3}+\cdots\)
363.3.b.i \(4\) \(9.891\) \(\Q(\sqrt{-2}, \sqrt{-7})\) None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-1+\beta _{3})q^{3}-3q^{4}+\beta _{3}q^{5}+\cdots\)
363.3.b.j \(6\) \(9.891\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(-3-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
363.3.b.k \(6\) \(9.891\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(-3+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
363.3.b.l \(8\) \(9.891\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(5\) \(0\) \(-28\) \(q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{3}-\beta _{5}+\beta _{6})q^{3}+\cdots\)
363.3.b.m \(8\) \(9.891\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(5\) \(0\) \(28\) \(q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{4}+\beta _{5})q^{3}+(-4+\cdots)q^{4}+\cdots\)
363.3.b.n \(12\) \(9.891\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-4\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-4+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(363, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(363, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)