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Properties

Label 368.7
Level 368
Weight 7
Dimension 14107
Nonzero newspaces 8
Sturm bound 59136
Trace bound 5

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Defining parameters

Level: \( N \) = \( 368 = 2^{4} \cdot 23 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(59136\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(368))\).

Total New Old
Modular forms 25652 14297 11355
Cusp forms 25036 14107 10929
Eisenstein series 616 190 426

Trace form

\( 14107 q - 40 q^{2} - 29 q^{3} - 220 q^{4} + 81 q^{5} + 980 q^{6} - 25 q^{7} - 1972 q^{8} - 1313 q^{9} + O(q^{10}) \) \( 14107 q - 40 q^{2} - 29 q^{3} - 220 q^{4} + 81 q^{5} + 980 q^{6} - 25 q^{7} - 1972 q^{8} - 1313 q^{9} + 2204 q^{10} - 2749 q^{11} + 4652 q^{12} + 7473 q^{13} - 15172 q^{14} - 33 q^{15} + 15908 q^{16} - 27943 q^{17} + 3704 q^{18} - 7901 q^{19} + 33084 q^{20} + 70449 q^{21} - 50548 q^{22} + 13091 q^{23} + 65096 q^{24} - 105773 q^{25} - 117948 q^{26} - 71585 q^{27} - 90396 q^{28} + 173137 q^{29} - 16948 q^{30} - 33 q^{31} + 79300 q^{32} - 101467 q^{33} + 105132 q^{34} + 224807 q^{35} + 276924 q^{36} + 149169 q^{37} + 374516 q^{38} - 508825 q^{39} - 330364 q^{40} - 98615 q^{41} - 707036 q^{42} + 535939 q^{43} - 761492 q^{44} - 430028 q^{45} - 248200 q^{46} - 66 q^{47} + 921604 q^{48} + 444723 q^{49} + 1439304 q^{50} - 603609 q^{51} + 1569740 q^{52} + 62641 q^{53} + 1095060 q^{54} + 465383 q^{55} - 732892 q^{56} + 236533 q^{57} - 2883868 q^{58} - 78333 q^{59} - 4811244 q^{60} - 2349903 q^{61} - 365708 q^{62} - 33 q^{63} + 637268 q^{64} + 1624237 q^{65} + 6785420 q^{66} + 245539 q^{67} + 5008756 q^{68} + 1013149 q^{69} + 2373544 q^{70} + 533991 q^{71} - 3497236 q^{72} - 1517879 q^{73} - 7220836 q^{74} + 6475739 q^{75} - 8492020 q^{76} - 5258327 q^{77} - 6358148 q^{78} - 4787673 q^{79} + 5797892 q^{80} - 2902901 q^{81} + 10009204 q^{82} + 2432531 q^{83} + 15205508 q^{84} + 12755521 q^{85} + 6480908 q^{86} + 9717039 q^{87} - 6616348 q^{88} - 711271 q^{89} - 20546844 q^{90} - 604836 q^{91} - 7253700 q^{92} - 4336006 q^{93} - 7718156 q^{94} - 11220561 q^{95} + 11378804 q^{96} - 8910487 q^{97} + 18353856 q^{98} - 12374509 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(368))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
368.7.d \(\chi_{368}(47, \cdot)\) 368.7.d.a 22 1
368.7.d.b 44
368.7.e \(\chi_{368}(137, \cdot)\) None 0 1
368.7.f \(\chi_{368}(321, \cdot)\) 368.7.f.a 1 1
368.7.f.b 2
368.7.f.c 8
368.7.f.d 12
368.7.f.e 12
368.7.f.f 36
368.7.g \(\chi_{368}(231, \cdot)\) None 0 1
368.7.k \(\chi_{368}(45, \cdot)\) n/a 572 2
368.7.l \(\chi_{368}(139, \cdot)\) n/a 528 2
368.7.o \(\chi_{368}(39, \cdot)\) None 0 10
368.7.p \(\chi_{368}(17, \cdot)\) n/a 710 10
368.7.q \(\chi_{368}(57, \cdot)\) None 0 10
368.7.r \(\chi_{368}(31, \cdot)\) n/a 720 10
368.7.u \(\chi_{368}(3, \cdot)\) n/a 5720 20
368.7.v \(\chi_{368}(5, \cdot)\) n/a 5720 20

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(368))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(368)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 1}\)