Properties

Label 105.2.b
Level $105$
Weight $2$
Character orbit 105.b
Rep. character $\chi_{105}(41,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $4$
Sturm bound $32$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 105.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(32\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(105, [\chi])\).

Total New Old
Modular forms 20 12 8
Cusp forms 12 12 0
Eisenstein series 8 0 8

Trace form

\( 12q - 16q^{4} - 8q^{7} - 2q^{9} + O(q^{10}) \) \( 12q - 16q^{4} - 8q^{7} - 2q^{9} + 2q^{15} + 8q^{16} - 4q^{18} + 6q^{21} + 8q^{22} + 12q^{25} + 16q^{28} + 4q^{30} - 36q^{36} - 16q^{37} + 30q^{39} + 36q^{42} - 40q^{43} - 16q^{46} + 12q^{49} - 30q^{51} - 12q^{57} + 8q^{58} - 36q^{60} - 44q^{63} - 8q^{64} + 24q^{67} + 64q^{72} + 84q^{78} + 36q^{79} + 22q^{81} - 36q^{84} - 12q^{85} + 16q^{88} - 12q^{91} + 12q^{93} + 26q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
105.2.b.a \(2\) \(0.838\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(4\) \(q-\zeta_{6}q^{2}-\zeta_{6}q^{3}-q^{4}-q^{5}-3q^{6}+\cdots\)
105.2.b.b \(2\) \(0.838\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(4\) \(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}-q^{4}+q^{5}+3q^{6}+\cdots\)
105.2.b.c \(4\) \(0.838\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-1\) \(-4\) \(-8\) \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+\beta _{1}q^{3}+(-1+\cdots)q^{4}+\cdots\)
105.2.b.d \(4\) \(0.838\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(1\) \(4\) \(-8\) \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}-\beta _{1}q^{3}+(-1+\cdots)q^{4}+\cdots\)