Properties

Label 750.2.l
Level $750$
Weight $2$
Character orbit 750.l
Rep. character $\chi_{750}(107,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $240$
Newform subspaces $3$
Sturm bound $300$
Trace bound $12$

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Defining parameters

Level: \( N \) \(=\) \( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 750.l (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 3 \)
Sturm bound: \(300\)
Trace bound: \(12\)
Distinguishing \(T_p\): \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(750, [\chi])\).

Total New Old
Modular forms 1360 240 1120
Cusp forms 1040 240 800
Eisenstein series 320 0 320

Trace form

\( 240q - 4q^{3} - 4q^{7} + O(q^{10}) \) \( 240q - 4q^{3} - 4q^{7} + 4q^{12} + 60q^{16} + 8q^{18} + 40q^{19} + 36q^{22} - 4q^{27} + 16q^{28} - 4q^{33} + 40q^{34} + 24q^{37} + 40q^{39} + 4q^{42} + 24q^{43} + 4q^{48} + 64q^{57} - 20q^{58} - 64q^{63} - 96q^{67} - 140q^{69} - 8q^{72} - 100q^{73} - 100q^{78} - 80q^{79} - 120q^{81} - 96q^{82} - 60q^{84} - 80q^{87} - 4q^{88} - 12q^{93} + 32q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(750, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
750.2.l.a \(80\) \(5.989\) None \(0\) \(-4\) \(0\) \(-4\)
750.2.l.b \(80\) \(5.989\) None \(0\) \(-4\) \(0\) \(-4\)
750.2.l.c \(80\) \(5.989\) None \(0\) \(4\) \(0\) \(4\)

Decomposition of \(S_{2}^{\mathrm{old}}(750, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(750, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(375, [\chi])\)\(^{\oplus 2}\)