Properties

Label 152.2.c
Level $152$
Weight $2$
Character orbit 152.c
Rep. character $\chi_{152}(77,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $2$
Sturm bound $40$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 152.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(40\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(152, [\chi])\).

Total New Old
Modular forms 22 18 4
Cusp forms 18 18 0
Eisenstein series 4 0 4

Trace form

\( 18q - 2q^{2} + 2q^{4} + 6q^{6} - 4q^{7} - 8q^{8} - 18q^{9} + O(q^{10}) \) \( 18q - 2q^{2} + 2q^{4} + 6q^{6} - 4q^{7} - 8q^{8} - 18q^{9} - 8q^{10} + 4q^{12} - 6q^{16} - 4q^{17} + 14q^{18} + 8q^{20} + 12q^{22} - 4q^{23} + 6q^{24} - 14q^{25} - 6q^{26} - 14q^{28} + 4q^{30} - 12q^{32} - 4q^{34} + 8q^{36} + 8q^{39} + 28q^{40} + 4q^{41} - 2q^{42} - 12q^{44} - 44q^{46} + 20q^{47} + 36q^{48} + 18q^{49} + 2q^{50} - 34q^{54} + 16q^{55} - 40q^{56} + 42q^{58} - 28q^{60} - 20q^{63} + 14q^{64} + 16q^{65} - 24q^{66} - 26q^{68} - 32q^{70} + 24q^{71} + 12q^{72} - 20q^{73} + 56q^{78} - 40q^{79} + 4q^{80} + 2q^{81} + 64q^{84} + 56q^{86} - 48q^{87} + 24q^{88} - 4q^{89} + 12q^{90} + 62q^{92} - 32q^{94} + 16q^{95} - 70q^{96} + 12q^{97} - 42q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(152, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
152.2.c.a \(2\) \(1.214\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(4\) \(q+(-1+i)q^{2}-2iq^{4}+2q^{7}+(2+2i)q^{8}+\cdots\)
152.2.c.b \(16\) \(1.214\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-8\) \(q+\beta _{9}q^{2}+\beta _{4}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots\)