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Properties

Label 36.3.d
Level $36$
Weight $3$
Character orbit 36.d
Rep. character $\chi_{36}(19,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $3$
Sturm bound $18$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 36.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(18\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(36, [\chi])\).

Total New Old
Modular forms 16 6 10
Cusp forms 8 4 4
Eisenstein series 8 2 6

Trace form

\( 4 q + 2 q^{2} + 4 q^{4} + 4 q^{5} - 16 q^{8} + O(q^{10}) \) \( 4 q + 2 q^{2} + 4 q^{4} + 4 q^{5} - 16 q^{8} - 28 q^{10} - 16 q^{13} + 24 q^{14} + 16 q^{16} - 20 q^{17} - 8 q^{20} + 24 q^{22} + 36 q^{25} + 4 q^{26} + 48 q^{28} + 52 q^{29} + 32 q^{32} + 44 q^{34} - 88 q^{37} - 72 q^{38} - 160 q^{40} - 116 q^{41} + 48 q^{44} - 96 q^{46} + 100 q^{49} - 42 q^{50} - 88 q^{52} + 148 q^{53} + 212 q^{58} + 8 q^{61} - 24 q^{62} + 256 q^{64} + 8 q^{65} + 40 q^{68} + 48 q^{70} + 128 q^{73} + 52 q^{74} - 144 q^{76} - 96 q^{77} - 32 q^{80} - 436 q^{82} - 296 q^{85} + 168 q^{86} - 164 q^{89} - 192 q^{92} + 240 q^{94} - 256 q^{97} + 2 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(36, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
36.3.d.a \(1\) \(0.981\) \(\Q\) \(\Q(\sqrt{-1}) \) \(-2\) \(0\) \(8\) \(0\) \(q-2q^{2}+4q^{4}+8q^{5}-8q^{8}-2^{4}q^{10}+\cdots\)
36.3.d.b \(1\) \(0.981\) \(\Q\) \(\Q(\sqrt{-1}) \) \(2\) \(0\) \(-8\) \(0\) \(q+2q^{2}+4q^{4}-8q^{5}+8q^{8}-2^{4}q^{10}+\cdots\)
36.3.d.c \(2\) \(0.981\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(4\) \(0\) \(q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{4}+2q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(36, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(36, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)