Properties

Label 363.2.f
Level $363$
Weight $2$
Character orbit 363.f
Rep. character $\chi_{363}(161,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $112$
Newform subspaces $9$
Sturm bound $88$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 363.f (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 9 \)
Sturm bound: \(88\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(5\), \(7\)

Dimensions

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

Total New Old
Modular forms 224 176 48
Cusp forms 128 112 16
Eisenstein series 96 64 32

Trace form

\( 112 q + 7 q^{3} - 14 q^{4} + 10 q^{7} - 11 q^{9} + O(q^{10}) \) \( 112 q + 7 q^{3} - 14 q^{4} + 10 q^{7} - 11 q^{9} - 68 q^{12} + 10 q^{13} + 9 q^{15} - 2 q^{16} - 20 q^{19} + 10 q^{24} - 28 q^{25} + 16 q^{27} + 20 q^{30} + 26 q^{31} - 24 q^{34} + 16 q^{36} + 8 q^{37} - 20 q^{39} - 60 q^{42} - 100 q^{45} - 30 q^{46} - 6 q^{48} - 50 q^{49} - 30 q^{51} - 10 q^{52} + 30 q^{57} - 28 q^{58} + 44 q^{60} + 10 q^{61} + 30 q^{63} + 86 q^{64} - 68 q^{67} + 11 q^{69} + 34 q^{70} + 20 q^{72} + 24 q^{75} - 12 q^{78} - 50 q^{79} + 5 q^{81} + 6 q^{82} - 10 q^{85} - 40 q^{90} + 54 q^{91} - 13 q^{93} + 30 q^{94} - 10 q^{96} - 52 q^{97} + O(q^{100}) \)

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.f.a $8$ $2.899$ 8.0.64000000.1 None \(-2\) \(-2\) \(0\) \(0\) \(q-\beta _{6}q^{2}+(-1+\beta _{2}-\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots\)
363.2.f.b $8$ $2.899$ \(\Q(\zeta_{20})\) None \(0\) \(-6\) \(0\) \(10\) \(q+(-\zeta_{20}^{5}-\zeta_{20}^{7})q^{2}+(-1-\zeta_{20}+\cdots)q^{3}+\cdots\)
363.2.f.c $8$ $2.899$ 8.0.228765625.1 \(\Q(\sqrt{-11}) \) \(0\) \(-1\) \(0\) \(0\) \(q-\beta _{1}q^{3}-2\beta _{7}q^{4}+(-\beta _{4}-2\beta _{5})q^{5}+\cdots\)
363.2.f.d $8$ $2.899$ \(\Q(\zeta_{20})\) None \(0\) \(4\) \(0\) \(10\) \(q+(-\zeta_{20}-\zeta_{20}^{7})q^{2}+(1+\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots\)
363.2.f.e $8$ $2.899$ \(\Q(\zeta_{20})\) None \(0\) \(4\) \(0\) \(-10\) \(q+(-\zeta_{20}-\zeta_{20}^{7})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots\)
363.2.f.f $8$ $2.899$ 8.0.64000000.1 None \(2\) \(-2\) \(0\) \(0\) \(q+(1-\beta _{2}+\beta _{4}-\beta _{6})q^{2}+(\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
363.2.f.g $16$ $2.899$ 16.0.\(\cdots\).7 \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{5}-\beta _{10}-\beta _{13})q^{3}+2\beta _{4}q^{4}+\cdots\)
363.2.f.h $16$ $2.899$ 16.0.\(\cdots\).1 None \(0\) \(6\) \(0\) \(0\) \(q+(\beta _{2}-2\beta _{6}-\beta _{8}+\beta _{12}+\beta _{13})q^{2}+\cdots\)
363.2.f.i $32$ $2.899$ None \(0\) \(4\) \(0\) \(0\)

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

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