Properties

Label 363.2.e
Level $363$
Weight $2$
Character orbit 363.e
Rep. character $\chi_{363}(124,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $72$
Newform subspaces $14$
Sturm bound $88$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 363.e (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 14 \)
Sturm bound: \(88\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(363, [\chi])\).

Total New Old
Modular forms 224 72 152
Cusp forms 128 72 56
Eisenstein series 96 0 96

Trace form

\( 72q + 4q^{2} - 14q^{4} + 4q^{5} + 2q^{6} + 2q^{7} - 8q^{8} - 18q^{9} + O(q^{10}) \) \( 72q + 4q^{2} - 14q^{4} + 4q^{5} + 2q^{6} + 2q^{7} - 8q^{8} - 18q^{9} - 4q^{10} + 8q^{12} + 2q^{13} + 6q^{14} - 2q^{15} - 22q^{16} - 14q^{17} - 6q^{18} + 20q^{19} + 2q^{20} - 16q^{21} - 4q^{23} - 12q^{24} - 20q^{25} + 2q^{26} + 12q^{28} + 4q^{29} + 8q^{31} + 48q^{32} - 56q^{34} - 14q^{36} - 2q^{37} + 14q^{38} + 16q^{39} - 4q^{40} - 20q^{41} + 14q^{42} - 16q^{43} + 4q^{45} - 10q^{46} - 6q^{47} - 8q^{48} - 16q^{49} - 18q^{50} - 10q^{52} - 6q^{53} - 8q^{54} - 108q^{56} + 44q^{58} + 46q^{59} + 12q^{60} + 18q^{61} + 28q^{62} + 2q^{63} + 2q^{64} + 28q^{65} - 44q^{67} + 28q^{68} + 10q^{69} + 34q^{70} + 32q^{71} + 2q^{72} - 20q^{73} + 30q^{74} - 40q^{76} - 64q^{78} + 6q^{79} + 14q^{80} - 18q^{81} + 46q^{82} - 34q^{83} + 2q^{85} + 24q^{86} - 24q^{87} - 60q^{89} - 4q^{90} - 18q^{91} + 22q^{92} - 56q^{93} - 18q^{94} - 30q^{95} + 8q^{96} + 10q^{97} - 40q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(363, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
363.2.e.a \(4\) \(2.899\) \(\Q(\zeta_{10})\) None \(-5\) \(-1\) \(-2\) \(-10\) \(q+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
363.2.e.b \(4\) \(2.899\) \(\Q(\zeta_{10})\) None \(-4\) \(1\) \(2\) \(-1\) \(q+(-2+\zeta_{10}-\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots\)
363.2.e.c \(4\) \(2.899\) \(\Q(\zeta_{10})\) None \(-2\) \(-1\) \(4\) \(3\) \(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}+\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots\)
363.2.e.d \(4\) \(2.899\) \(\Q(\zeta_{10})\) None \(-2\) \(1\) \(-4\) \(1\) \(q+(-2+2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots\)
363.2.e.e \(4\) \(2.899\) \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(2\) \(-4\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
363.2.e.f \(4\) \(2.899\) \(\Q(\zeta_{10})\) None \(1\) \(1\) \(-3\) \(-1\) \(q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
363.2.e.g \(4\) \(2.899\) \(\Q(\zeta_{10})\) None \(1\) \(1\) \(2\) \(4\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
363.2.e.h \(4\) \(2.899\) \(\Q(\zeta_{10})\) None \(2\) \(-1\) \(4\) \(-3\) \(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots\)
363.2.e.i \(4\) \(2.899\) \(\Q(\zeta_{10})\) None \(2\) \(1\) \(-4\) \(-1\) \(q+(2-2\zeta_{10}+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+\cdots\)
363.2.e.j \(4\) \(2.899\) \(\Q(\zeta_{10})\) None \(3\) \(-1\) \(-1\) \(3\) \(q+(1-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
363.2.e.k \(4\) \(2.899\) \(\Q(\zeta_{10})\) None \(4\) \(1\) \(2\) \(1\) \(q+(2-\zeta_{10}+\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
363.2.e.l \(4\) \(2.899\) \(\Q(\zeta_{10})\) None \(5\) \(-1\) \(-2\) \(10\) \(q+(1+\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots\)
363.2.e.m \(8\) \(2.899\) 8.0.324000000.3 None \(0\) \(2\) \(6\) \(0\) \(q+\beta _{7}q^{2}-\beta _{6}q^{3}+\beta _{4}q^{4}+(3+3\beta _{2}+\cdots)q^{5}+\cdots\)
363.2.e.n \(16\) \(2.899\) 16.0.\(\cdots\).3 None \(0\) \(-4\) \(-2\) \(0\) \(q-\beta _{12}q^{2}+\beta _{4}q^{3}+(\beta _{3}-\beta _{6}+\beta _{8}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(363, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(363, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)