↑

Properties

Label 105.4.b
Level $105$
Weight $4$
Character orbit 105.b
Rep. character $\chi_{105}(41,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $2$
Sturm bound $64$
Trace bound $3$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(64\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(105, [\chi])\).

Total New Old
Modular forms 52 32 20
Cusp forms 44 32 12
Eisenstein series 8 0 8

Trace form

\( 32q - 128q^{4} - 8q^{7} - 44q^{9} + O(q^{10}) \) \( 32q - 128q^{4} - 8q^{7} - 44q^{9} + 20q^{15} + 752q^{16} - 364q^{18} - 144q^{21} - 552q^{22} + 800q^{25} + 20q^{28} + 280q^{30} + 1992q^{36} - 1624q^{37} - 1188q^{39} - 2808q^{42} - 1096q^{43} + 2448q^{46} + 656q^{49} + 1500q^{51} + 864q^{57} + 1152q^{58} + 660q^{60} - 536q^{63} - 8000q^{64} + 2008q^{67} + 900q^{70} + 3976q^{72} + 2892q^{78} + 2584q^{79} - 5900q^{81} + 648q^{84} + 720q^{85} - 1824q^{88} - 1104q^{91} - 2160q^{93} + 5060q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
105.4.b.a \(16\) \(6.195\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-2\) \(-80\) \(-4\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-4+\beta _{2})q^{4}-5q^{5}+\cdots\)
105.4.b.b \(16\) \(6.195\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(2\) \(80\) \(-4\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-4+\beta _{2})q^{4}+5q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)